NEW YORK — Asian action star Jackie Chan has been often compared to Buster Keaton (no one takes a fall better) and sometimes to Douglas Fairbanks (whose acrobatic grace he equals in vaulting over a wall). But I’m always fascinated by his moves: Chan is the Fred Astaire of outrageous mayhem.

A child who, starting at age 7, attended an academy for Chinese opera and martial arts in his native Hong Kong, Chan was an international star well before he came to the attention of most American moviegoers. His breakthrough film, “Police Story” (1985), and its inevitable first sequel, “Police Story II” (1988), both digitally restored, are playing together at the Alamo Drafthouse in Brooklyn.

A small part alongside Burt Reynolds in “The Cannonball Run” (1981) failed to ignite Chan’s career in the United States. Until “Police Story” was included in the 1987 New York Film Festival, his New York fans often went to Chinatown’s movie houses to enjoy his comic windmill kick-box, karate-chop, tumble-out-of-a-third-story-window thing.

The incongruity of screening this violent slapstick at Lincoln Center was not lost on The New York Times critic Vincent Canby, who advised those who missed the festival shows that they could “catch up with more or less the same kind of thing on virtually any day of the week on 42d Street, where comic kung fu movies are treated not as cinematic epiphanies but as unpretentious comedies for people whose minds, like their feet, wander when not nailed to the floor.”

Indeed, “Police Story” — which Chan directed as well as starred in as a diligent but absent-minded cop — would be little more than a bang-bang procedural were it not for a number of impossibly kinetic set pieces. The scene in which Chan, who did all of his own stunts, employs the handle of an umbrella to hang on to a moving bus is easier to describe than the gyrations he uses to confound six bad guys armed with clubs or ride a large shopping mall chandelier down to the ground. The sound of broken glass is Chan’s theme song. His directorial stunts are epitomized by a choreographed sequence that destroys an entire hillside shantytown.

“Police Story” is largely the sum of its action scenes although it’s also enjoyable to watch the villains wield cellphones the size of cinder blocks, or see the very young Maggie Cheung as Chan’s long-suffering girlfriend. (Brigitte Lin, another leading Hong Kong star, is also in the movie as the witness whom Chan’s police officer must protect.)

“Police Story II,” showing as a separate admission, appears never to have been reviewed in The Times. Production values are higher and the havoc quotient is lower, despite several elaborate explosions. The tiresome toilet humor is partly compensated for by some impressively orchestrated gags — involving chain reactions worthy of Rube Goldberg — and a fireworks display that brings down the abandoned factory where the final battle is staged.

The best part of a Chan production can be the humorous montage of outtakes that accompany the closing credits. As if to offset the diminished violence in “Police Story II,” the coda shows real injuries and actual blood.

— Event info: Police Story and Police Story II, Alamo Drafthouse, Downtown Brooklyn, 718-513-2547, drafthouse.com. Also streaming on platforms including YouTube, Vudu and GooglePlay.

This article originally appeared in The New York Times.