Oliver, a laid-off IBM worker, leaves his homeless shelter on that fateful Sunday to walk the streets and spend yet another day trying to figure out how he got to the point where he is and how to get out of it. Madeleine, an out-of-work, middle-aged actress, is similarly grappling with her future after a divorce and looming custody fight. These two lost souls just happen to be walking on the same street when Madeleine sees Oliver and believes him to be the famous film director Matthew Delacorta. She introduces herself to him, and Oliver plays along with her belief that he is someone other than himself. They soon end up in her apartment, where they make love and spend the rest of the day together.

But the deception of Oliver's identity is a two-way street. As the day progresses, it becomes clear that Madeleine desperately wants to believe that Oliver is Matthew just as badly as Oliver does. And, as time passes, both their identities--real and assumed--seem to matter less and less in the face of the emotional connection the couple reaches.

With such a quietly subtle script, the strength of Sunday is that it is filmed in such a way that energy permeates the movie. The bustle of morning at the homeless shelter, the lively streets of Queens and the clutter of Madeleine's apartment are photographed so that they become almost exotic locales for what is essentially a love story. The soundtrack is also extremely effective: Stately opera music plays as the camera takes in lowly butcher shops and subways.

Naturally, the actors who play the two main roles in a film like this bear a huge burden. Lisa Harrow plays Madeleine with a skittish intensity that suits her character perfectly. And David Suchet as Oliver/Matthew is simply phenomenal. Best known for playing Hercule Poirot in PBS's Agatha Christie series, Suchet here plays the polar opposite of a debonair detective with surprising skill. Director Jonathan Nossiter asked Suchet to put on 47 pounds for Sunday, which he did for a role that has several nude scenes.

One of the most interesting things about Sunday is its unsettling ending. Without giving too much away, the movie disconcerts because it does the exact opposite of what you might expect. There is no grand climactic scene where Oliver is dramatically exposed for what he is while Madeleine is shocked and horrified. Instead, the events merely unfold, and the viewer is left to come to his or her own conclusions about the couple's relationship.