Both species cannot have the other as a primary source of food. Due to the inefficiencies of trophic energy transfer, there fundamentally needs to be a lot more prey than predators. An ecosystem of only two predators preying on one another would be like a biological perpetual motion machine.

At least one of the species must have another primary source of food. You might have isolated instances of bi-directional predation, but there's no way a species can be sustained by consuming a species that preys on it. One of the predators must find another prey - and given the choice of a meal that might eat you back and one that won't, there is a very strong pressure to prey upon the species that won't try to eat you.

Theoretically Yes

If we imagine one of the predators as a R-class reproduction species of solitary hunters and the other as pack hunters, along with a supply of massive herbivores for both to hunt alongside each other, you could get this to happen.

Species R is something akin to a Tyrannosaurus Rex. They're big, nasty, and take 30-40 years to reach full size. It has plenty of babies that are left to fend for themselves until birth which steadily grow from chicken-sized to multi-ton predators.

Species P is a big pack hunter. Utahraptors, Dire wolves, something along those lines. They need to be big enough to take out massive prey while still being individually the right size for a multi-ton predator to consider a meal.

Species P preferentially hunts Species R when it's subadult, but eventually Species R gets too big and nasty to be worth the risk. Species R eventually gets SO big that it hunts and eats Species P (presumably along with other things roughly their size). Of course, as Species R gets bigger and bigger, they naturally get slower and less agile, eventually turning away from hunting Species P to go after less nimble prey. At a certain point in its life Species R gets so ungainly that Species P packs can target Species R and successfully bring them down at the same rate and risk as they can other megafauna.

These species would then both be preying on adults, though it remains something of a cycle of predation with overlap rather than "adults of both species hunt each other all the time."

Habitats swing.

As in there is plenty, then there is little. It might be due to prey population collapse or nature synchronizing to have better chances at offspring. https://en.wikipedia.org/wiki/Pannage is an example, where tree synchronize to have offspring at the same time to increase the chanes. Thus the boar- which predator and prey at the same time, increases cyclical with these cycles.

Thus everything predating a boar, living in a habitat that cyclical swings- would evolutionary benefit from going insane. As in- loopdeform the species (by epigentics or genetics directly)- and behavioural adapt to these swinging habitats. Its absolutly insane, to not overreproduce and live as if the good times last forever in pannage valleys. Its absolutly insane, to be not paranoid and forgiving at the same time in the wanning times and in the recovery times. Its absolutly insane to not eat others and whatever comes along in the peak of the valley of the boar, when your population peaks and fights for ever slimmer pickings. Thus a species could split in two or threes.

One phenotype is adapted to the valleys, and forever peacefull- thus the perfect prey. The other, which hold its feet still in those times, is hyper adapted to the horrific peak of the loop, where the other becomes a always "flee&survive" mess.

Both exist at the same time- and interact with similar creatures, similarly adapted at the same times. All are sane, as in adapted to a insane situation, the game-theory it presents. There might be even "inner-species" alliance instincts- as in - you suck at peace except as monster for movies, but we feed you, because you will protect our offspring in war times when we are worse then useless.

It's a Winter Survival Trait

In the warm months, there are lots of herbivores, the predators hunt the herbivores and rapidly grow in number. They both reproduce quickly knowing most will not survive the winter when the prey animals all migrate away leaving the predators to starve. Neither species can survive without turning to eating what is left, and both species have strong anti-cannibalistic instincts (maybe they both need a different essential nutrient that they don't produce themselves and can't get from cannibalism); so, they will only eat each other to survive. Each hunt is individually dangerous but one way or another, someone will survive long enough to make it to the next spring to begin reproducing again.

What keeps it a stable system is that if in one winter a lot more of predator A wins, then in the next winter there will be a lot less predator B to survive off of so A will starve off while B will have a lot of A to feed on allowing the B population to recover.

there is a way but several things need to be true.

1. they both must be R strategists.

2. both mostly predate other things, possibly mostly as young with the adults focusing on the young of the other.

3. it helps a lot if they hunt in different methods, AKA jaguar and crocodiles.so A looses on B's terrian and B losses on A terrian.

basically you are setting up a bromeliad frogs and algea situation but with two species. If you don't know bromeliad frogs have one of the simplies ecosystems the tadpoles eat algae and the adults eat tadpoles. you are just doing this with two species eating each others offspring. They need a large source of outside energy so either they young are primary consumers or their is abundant small prey for them to act as small predators.

Your biggest problem is is becomes very easy for one to wipe the other out. The systm is unstable, fewer A leads to more B which eat more A. so you need safe places for young, so they can never be wiped out. If you add some third factor that makes fewer of one impact prey soecies negativly that helps. Maybe both contribute in some way to creating the eviroment like beavers but with two species doing different parts of the work. Or the primary prey of young A needs somthing B does B and vice versa. thay way any time one dips too low the other predators suffers.

I think if there are two large species of ambush predators in your ecosystem it will be fairly common for either species to prey on the other species. Members of species A may eat members of species B about as often as members of species B eat members of species A.

I note that it is common for large predators to prey on small predators in addiiton to herbivores. There is no predator code that prevents larger predators from preying on smaller predators.

There are many species of predators where adults will sometimes prey on smaller and younger members of their own species. Obviously if they prey on smaller members of their own species they will prey on smaller members of closely related predator species and smaller members of very different predator species, as well as on smaller herbivores and omnivores.

For example, one time a great blue heron swallowed a snake at our pond, and snakes are all predators. Large pythons sometimes swallow small crocodilians and you can find photos of that on the internet.

Our pond was stocked with bass and bluegills. Bluegills eat smaller acquatic lifeforms and bass each bluegills as well as the smaller animals that bluegills eat. And bluegills probably eat baby bass.

You have probably seen drawings showing a small fish about to be eaten by a larger fish which is about to be eaten by third fish about to be eaten by a fourht fish, etc.

I note human hunter-gatherers get a lot of their food from preying on other animals, while civilized humans raise domestic animals to slaughter and eat and so are also partially predators. Humans mostly eat herbivorous animals, but sometimes eat other predators. My mother told me that when her brother was a boy at camp he shot and ate a rattlesnake.

So omniverous humans are partially pedators. Which means that any species of predators whose members sometimes prey on humans are capable of preying on other predators.

Here is a link to an article discussing many species who sometimes prey on humans.

https://en.wikipedia.org/wiki/Man-eating_animal

Humans often hunt members of those species, and sometimes eat them.

In the ocean, the larger carniverous sharks are apex predators. Toothed whales are also apex predators. But basking sharks and whale sharks, and the baleen whales, who are all filter feeders, can also be considered predators, since the small lifeforms which they filter out of the water include both plants and animals.

So not only the larger carniverous sharks and the toothed whales are apex predators of the sea. filter feeding sharks and whales can also be considered apex predators of the sea.

And so there are examples of apex sea predators preying on other apex sea predators.

"Humans are the biggest threat to bull sharks. Larger sharks, such as the tiger shark and great white shark, may attack them, but typically only target juveniles.2 Crocodiles may be a threat to bull sharks in rivers. Saltwater crocodiles have been observed preying on bull sharks in the rivers and estuaries of Northern Australia,[67] and a Nile crocodile was reportedly sighted consuming a bull shark in South Africa.[68]"

https://en.wikipedia.org/wiki/Bull_shark#Ecology

"Basking sharks have few predators. White sharks have been reported to scavenge on the remains of these sharks. Killer whales have been observed feeding on basking sharks off California in the US and New Zealand."

https://en.wikipedia.org/wiki/Basking_shark#Predators

"Tiger sharks are preyed on by orcas. Orcas have been recorded hunting and killing tiger sharks by holding them upside down to induce tonic immobility in order to drown the shark. The orcas bite off the shark's fins before disemboweling and devouring it.5"

https://en.wikipedia.org/wiki/Tiger_shark#Predation_by_orcas

"White sharks are sometimes preyed on by orcas, with which they also likely compete with for food.[106] The first recorded orca predation occurred at the Farallon Islands in 1997 when an estimated 4.7–5.3 m (15–17 ft) female orca killed an estimated 3–4 m (10–13 ft) white shark.[135] Another similar attack apparently occurred there in 2000, but its outcome is not clear.[136] Orca predation has since been documented on white sharks in other areas.[137][138] Around South Africa, orcas typically hunt white sharks in groups of two to six.[139] By flipping the sharks belly up, the whales trigger a paralytic state known as tonic immobility, allowing them to precisely target and consume the sharks' energy-rich livers.[140] In 2017, a live white shark was sighted with purported orca teeth marks, providing the first evidence of the species surviving such an attack.[141] White sharks often evacuate an area when orcas arrive, as has been documented both off South Africa and California.[138][142] However, a 2026 study near Neptune Islands concluded that orcas alone are unlikely to cause white sharks to leave an area long-term.[143] In addition to orcas, white sharks may fall prey to other sharks, including older white sharks, as pups and juveniles.[64]"

https://en.wikipedia.org/wiki/Great_white_shark#Mortality_and_health

The largest of all animals, and thus the largest sort of predator, is the blue whale.

"There is no well-documented natural predator of blue whales. The only documented attacks on blue whales involve orcas. Because killing a blue whale requires considerable effort and coordination, orcas often target calves. The rate of fatal attacks by orcas is unknown.

Photograph-identification studies of blue whales have estimated that a number of the individuals in the Gulf of California have rake-like scars, indicative of encounters with orcas.[131] Off southeastern Australia, 3.7% of blue whales photographed had rake marks and 42.1% of photographed pygmy blue whales off Western Australia had rake marks.[132] A blue whale mother and calf were first observed being chased at high speeds by orcas off southeastern Australia.[133] The first documented attack occurred in 1977 off southwestern Baja California, Mexico, but the injured whale escaped after five hours.[134] Four more blue whales were documented as being chased by a group of orcas between 1982 and 2003.[135] In September 2003, a group of orcas in the Eastern Tropical Pacific was encountered feeding on a recently killed blue whale calf.[136] In March 2014, a commercial whale watch boat operator recorded an incident involving a group of orcas harassing a blue whale in Monterey Bay. The blue whale defended itself by slapping its tail.[137] A similar incident was recorded by a drone in Monterey Bay in May 2017.[138] The first direct observations of orca attacks occurred off the south coast of Western Australia, two in 2019 and one more in 2021. The first victim was estimated to be an adult between 18–22 meters (59–72 ft).[139]"

https://en.wikipedia.org/wiki/Blue_whale#Predators

"The most common natural predator of sperm whales is the orca (killer whale), but pilot whales and false killer whales sometimes harass them.[213][214] Orcas prey on target groups of females with young, usually making an effort to extract and kill a calf. The females will protect their calves or an injured adult by encircling them."

https://en.wikipedia.org/wiki/Sperm_whale#Ecology

Large male sperm whales can easily kill any shark or any other toothed whale, under the right circumstances such as ambushing one and disabling it with the first strike.

The only limit to the size of creatures which sperm whales eat is that sperm whales have to swallow their prey whole. They don't bit smaller chunks out of their prey, though I guess a group could pull a prey animal apart into smaller pieces.

Even though sperm whales don't bite off pieces of their prey, their bite is very dangerous. They have bitten small wooden boats in half. They can crush bones and internal organs with their jaws, and probably chomp on larger prey a few times to soften it so it is flexible enough to go down their throats and they don't choke on it. So entire sharks, some rather large, have been found in sperm whale stomachs. I think that sperm whales could swallow smaller and medium specimens of bull sharks, megamouth sharks, Greenland sharks, tiger sharks, and great white sharks, if not the larger specimens. And of course they could swallow babies of any shark species.

Sperm whales rarely eat other mammals, perhaps only by mistake, and so they aren't known to hunt seals, dolphins, and other whale species. A sperm whale could kill and eat a lone baby killer whale, unprotected by others in their pod, if it decided to. Under the right cirumstances a large male sperm whale would have a fair chance to kill any of the great whales or a megalodon, but probably wouldn't have a reason to try it.

So all of the largest predators in the sea can potentially prey on the other largest predators in the sea. And some of them do prey on some of the other largest predators in the sea.

I think that it is perfectly possible for two large predator species to prey on each other. The adults of species A may prey on young of species B, as well as other species, while adults of species B prey on young of species A,aswell as other species. And possibly extremly large adults of either species can prey on small or normal sized adults of the other species.

Many animals are ambush predators, which wait in hiding until prey comes near and then attack swiftly before the prey can react. Thus ambush predators can kill and eat animals as large and dangerous as themselves, and sometimes animals much larger than themselves.

Thus I can imagine an ecosystem with two or more large apex predators which are both ambush predators and thus each of them sometimes preys on members of the other species.

No, by definition

An apex predator is, by definition, the predator in a food web that does not have other habitual predators.

Therefore you can't describe them as apex predators if they habitually predatate each other.

Biology is pretty fuzzy, though - there's not really a reason two species, who both eat other things and each other, can't be competing for the spot of apex predator.

In reality we also see a lot more fuzziness - for example, baby sharks are eaten by a bunch of things, including other sharks. But fully grown great white sharks would be an apex predator in some ecosystems, so the term ends up being kind of odd, based on age and environment.