In this screen adaptation of the award-winning play by Herb Gardner (who also directed the film), Nat Moyer (Walter Matthau) and Midge Carter (Ossie Davis) are two elderly men who sit on the same park bench each afternoon and have developed a relationship based on playful verbal sparring.
Nat is an eccentric Jewish leftist who uses a dizzying variety of voices and assumed personalities to get his way, while Midge is the African-American superintendent of an apartment building who is afraid that he's going to be put out to pasture, as he's about to turn 80. Nat tries to encourage Midge to join him in his good-natured con games (which are performed for good causes and not for profit), but Midge remains wary.
While Midge sweats out a possible retirement, Nat is trying to deal with his daughter Clara (Amy Irving), who wants to put him in a nursing home.
Meanwhile, a drug dealer called The Cowboy (Craig T. Nelson) has claimed the park as his own territory, and Nat, impersonating a Mafia don, tries to run him out, while he befriends Laurie (Martha Plimpton), a young woman hooked on dope.