"The Lake House," a wondrously illogical time-travel romance directed by Alejandro Agresti, is notable mainly for reuniting Keanu Reeves and Sandra Bullock, who together survived a harrowing bus ride in "Speed." That was 12 years ago ¡ª how time flies! ¡ª and since then they have gone their separate movie-star ways, into the "Miss Congeniality" and "Matrix" franchises, as well as into a startlingly long list of bad movies, of which I will mention only "Hope Floats" and "Sweet November."

But these two stars have a habit of being more appealing than their material. This is not just a matter of excellent facial bone structure, but also of a sly ability to play simultaneously in and against type. Because Ms. Bullock and Mr. Reeves have become such familiar screen presences, their performances turn out, more often than not, to be genuinely surprising. Ms. Bullock likes to be difficult, to temper her radiance with grouchiness, while Mr. Reeves, when the mood strikes, can inflect his mild, baffled affect with meanness, moodiness and even a hint of thorny intelligence.

So while the general public has not, as far as I can tell, been clamoring for a reunion, "The Lake House" nonetheless functions as a fascinating experiment. Is the chemistry ¡ª or, given that "Speed" was all about the velocity of bodies in motion, the physics ¡ª still there? It is, although in this case the viewer will also have to grapple with a heavy dose of Hollywood metaphysics, which keeps the leads apart for most of the movie.

At the start, Ms. Bullock's character, Kate, a stressed-out physician who has just completed her residency, moves out of the architectural curiosity that gives the picture its title, leaving a note in the mailbox for the next tenant. That would be Mr. Reeves's Alex, a soulful real estate developer who turns out actually to be the previous tenant. Some unexplained wrinkle in the space-time continuum ¡ª or a serious glitch at the postal service ¡ª has made it possible for Kate, in 2006, to correspond with Alex, who is still making his way through 2004.

"Not much has changed," Kate writes to him at one point, when he asks what things are like in the future. His general lack of curiosity ¡ª he doesn't ask who won the presidential election or the World Series, or pester her for stock market tips ¡ª is in keeping with the fuzziness of the film's conceit. If you approach it with a rational, skeptical mind, "The Lake House" will fall apart almost immediately. But where is the fun in that? You'll just have to accept that a book can travel through the mail to a date earlier than the one printed on its copyright page, and that a fancy Chicago restaurant will hold an unconfirmed reservation for two years.

"The Lake House," while completely preposterous, is not without charm. Both Kate and Alex drive well-preserved old cars ¡ª hers is a copper-colored Mustang that appears to be of late-60's vintage, while his pickup truck looks even older ¡ª and the movie they inhabit, based on a Korean film called "Il Mare," is an unapologetic throwback to a classic studio genre, the melodrama of impossible love. The social obstacles that used to exist ¡ª in the real world and, more intensely, in Production Code-governed Hollywood ¡ª have lost their forbidding power, which may be why supernatural and science fiction touches are required to keep the idea of romantic longing alive.

Kate and Alex, by means of handwritten letters placed in that mailbox (and read in back-and-forth voice- over to simulate real-time conversations), fall deeply and achingly in love. There is some competition for their affection. Alex is coolly, almost sadistically indifferent to a co-worker (Lynn Collins) who all but throws herself at his feet, while Kate has recently broken up with a perfectly decent but manifestly inadequate fianc¨¦ (Dylan Walsh), who keeps showing up no matter what year it is. She also has a gentle mother (Willeke van Ammelrooy) and a wise boss (Shohreh Aghdashloo), who serve as confidantes, while Alex is burdened with an imperious, narcissistic father (Christopher Plummer), a famous architect who designed that strange, impractical house by the lake.

The contrivances of the plot, which may require occasional glances at a multiyear date book, are smoothly handled by David Auburn's script and by Mr. Agresti's direction. Visually, "The Lake House" is elegant without being terribly showy, with a connoisseur's eye for Chicago's architectural glories. But the movie is, above all, a showcase for its stars, who seem gratifyingly comfortable in their own skin and delighted to be in each other's company again, in another deeply silly, effortlessly entertaining movie.

"The Lake House" is rated PG (Parental guidance suggested). It has occasional dark moods and sad moments, but no bad language or sex.