Psychological thrillers have become their own cliche over the years — shifting personalities, mistaken identities, questions of what is real and what is fantasy. And they all figure in "Enemy."

But this psychological thriller is also a thriller about psychology — or at least about one man's psychology. And it is as maddeningly elusive as it is endlessly, sneakily intriguing.

The story comes from the novel "The Double" by the Portuguese writer Jose Saramago, who in addition being a Nobel prize-winner was also the source of the similarly tricky movie "Blindness"; the film is directed by Denis Villeneuve, the talented French-Canadian who made last year's excellent "Prisoners."

It's a good match.

Although most Americans know Villeneuve only from that creepy thriller, if you saw it you know it was possibly the most unsettling serial-killer film since "Zodiac"; if you really looked at it, and saw his other films, you'd know themes of identity and funhouse-mirrored patterns of behavior fascinate him.

They're at the core of "Enemy," which begins when a dull, depressed history professor rents a movie and sees a bit actor who is his exact double. It shakes him — a little exaggeratedly, almost existentially — and he fearfully searches out the man who also shares his voice (and, it turns out, a similar blonde lover).

The two men, eventually, meet. Take turns stalking each other. And then, dangerously, begin to exchange lives.

You don't have to be Freud — or Jung, or even Alfred Hitchcock — to know that this is going to end badly.

Yet in this film, Villeneuve's inspirations seem to be closer to that premiere Canadian surrealist David Croenenberg, touched with a little David Lynch. He has a real ability to make the blandest Toronto cityscapes seem threatening, or the most passionate sex seem vile.

And through it all his camera snakes, slowly, slipping around corners, uncovering ugly things as the music builds.

Villeneuve's partner in all this is Jake Gyllenhaal who — apparently delighted to be in his trippiest film since "Donnie Darko" — commits utterly. His doubles are, of course, identical — yet each one has a slightly altered posture, a different cadence. They're like the same man, but in two different moods.

But is that what they are, really? A split personality? A fantasy? Long-lost twins? What's the answer here?

If anything, Villeneuve pushes the story even further into the enigmatic than Saramago did; there are occasional explosions of the inexplicable involving giant spiders, underground sex clubs, "crush porn" (don't ask) and naked women walking on the ceiling. It turns what should be metaphysical into a horror-movie nightmare, and I think it's a mistake.

But even if "Enemy" sometimes goes too far — and, in proffering any kind internal logic, never goes far enough — it grips your attention from the very first scene. And will haunt you long after its last.

Ratings note: The film contains sexual situations, nudity and strong language.

'Enemy' (R) A24 (90 min.)
Directed by Denis Villeneuve. With Jake Gyllenhaal. Now playing in New York.

★ ★ ★