Donnie Darko uses a style of story telling that is somewhat fragmented and which generates an uncertainty relating to truth or knowledge. Fragmented narratives and uncertainty of knowledge are both characteristics of post-modernism.
"For postmodernists [the response to modern life] took the guise of being self-conscious, experimental, and ironic. The postmodernist is concerned with imprecision and unreliability of language and with epistemology, the study of what knowledge is" (eNotes).
Opening the story with Donnie Darko (Jake Gyllenhaal) waking up in his pajamas far from home, the film offers uncertainty as its primary ethos as Donnie (we discover) has no idea what he is doing at night.
Unaware of his own actions, Donnie's character plays into a notion of fundamental epistemological flaws as part of the human condition. (How can he trust his sense of what is real and knowable if his own actions are unknowable? How can he come to understand the truth if his apparatus for understanding -- his self -- makes that impossible?)
The film builds on these ideas of uncertainty by connecting them to psychosis and to science fiction.
The fragmentary nature of the film can be identified in the scenes that depict the rabbit figure. These scenes break from the "natural," primary narrative and enter into dream. The act of trying to knit these fragments back into a natural order becomes one of the film's animating conflicts and drives the action (and the suspense) of much of the film.
Additionally, the film employs genre techniques from a number of film genres, thereby becoming something of a hybrid and imparting a subtle meta-narrative element to the film. The notion of narrative self-awareness (or textual self-awareness) that is inherent in meta-fiction and meta-narrative is another hallmark of post-modern style, demonstrating the idea that the story is a fiction and a product and so, again, questioning the notion of reality and truth that is offered within the body of the story.
Using some science fiction elements (time travel), "teen film" elements (the Halloween Dance) and music video elements in addition to an overarching suspense framework, the film implicitly takes on a self-awareness. Using multiple forms as Donnie Darko does constitutes a meta-narrative quality in the film. The film does a good job of successfully fusing these various genres and so avoids becoming overly confusing while achieving a sense of complexity and uncertainty.
Finally, paranoia is a tenet of a good deal of post-modernism. The idea that there may be a controlling force standing behind the visible world is on display in Donnie Darko in a number of ways. This is most plainly articulated in Donnie's views on Patrick Swayze's character.
“I'm pretty troubled and I'm pretty confused. And I'm afraid, really, really afraid, really afraid. But I think you're the [expletive] Antichrist.”
When Patrick Swayze's character is exposed as a pedophile, Donnie's suspicions are proved. This may seem to undermine the idea that paranoia was animating Donnie's beliefs, but the initial thought is paranoid as he trusts that an explanation exists for everything that happens and that dark forces are pulling the strings, unseen.
He is paranoid and he is right, but the film makes a strong statement as to the profound difficulties in coming to trust one's view of the world as a definitive take on what is real and true.