In 1952 Detroit, Michigan, three brothers, first-born Marvin, middle child Buddy, and little Bobby Libner share a bedroom and squabble constantly. Buddy's science project is destroyed during an altercation, and Marvin exclaims that he cannot wait to get away from the other two.
Eleven years later, in 1963, the adult Marvin (Daniel Stern), now a U.S. Air Force sergeant, arrives at a house to pick up a blue 1954 Cadillac Coupe de Ville convertible. At his father's request, he is supposed to drive it from Detroit to Miami, Florida, in time for his mother's 50th birthday. Buddy (Arye Gross) arrives and announces that their father asked him to accompany Marvin and pick up their younger brother, Bobby, at his high school academy, which Buddy calls a "reform school." Marvin and Buddy discuss whether it has been three or five years since they last saw each other. After Bobby (Patrick Dempsey) jumps into the back seat, he shouts obscenities at one of his teachers, but instead of driving away, Marvin forces Bobby to confront the teacher face to face.
Later, Marvin telephones their father, Fred Libner (Alan Arkin), from a gas station. Fred insists they deliver the car in perfect condition by Sunday afternoon in four days, and informs Buddy and Bobby that Marvin is in charge during the journey. Driving south, Marvin and Bobby argue over what to play on the radio. Marvin, the most conservative of the three, likes soft rock and roll, while the rebellious Bobby wants rhythm and blues. Bobby smokes a cigarette despite Marvin's objection and accidentally burns a hole in the back seat.
At a restaurant, Buddy and Bobby cannot believe Marvin is going to work with their inventor father after he leaves the Air Force. The brothers fight over the bill, and once they get back on the road, Buddy vomits in the back seat, egged on by Bobby. Meanwhile, in Florida, Fred Libner shows his brother, Phil Libner (Joseph Bologna), his latest invention, a plastic, rust-proof, lightweight stop sign that will last forever. He calls it an "annuity" for his sons. The two middle-aged brothers bicker until Phil leaves.
Meanwhile, Fred's three sons argue whether the car is the same blue 1954 Cadillac their father once owned, because why else would he want a nine-year-old car driven over a thousand miles to Florida? At a motel, Marvin, Buddy, and Bobby fight over whether to watch "The Fugitive" or Los Angeles Dodgers baseball on television.
The next day back on the road, a police car follows them, and when Bobby yells at him to speed up, Marvin hits a sign and smashes a headlight. The police pull them over and fine them $250. Marvin telephones their father, but does not reveal that they damaged the car and have run out of money. They sleep that night in the car on along the side of the road. Buddy confides to Bobby that in Florida he will see Tammy (Annabeth Gish), his college girl friend, who had sex with him on their first date. Buddy plans to ask her to marry him.
The next morning, Bobby reveals that he hid most of his money, but surrenders it to Marvin for gasoline. During an argument, Bobby accuses Marvin of being just like their father, grabs his bag, and walks away. Buddy convinces his kid brother to stay by assuring him they will never see each other again after delivering the car.
In Florida, as Fred Libner sits on his boat near his house, his wife, Betty (Rita Taggert), tells him she never regretted marrying him, despite the difficulties between them.
As the three younger Libners listen to The Kingsmen's recording of "Louie Louie" on the car radio, each one interprets the lyrics his own way. Bobby calls it a "hump song," Buddy a "dance song," and Marvin a "sea shanty." Later, while Marvin sleeps in the back seat, Buddy lets Bobby drive. Pushing what he thinks is the cigarette lighter, Bobby hits the button for the convertible top, and the wind rips it off the car.
A little later, as Buddy drives, he falls asleep, hits a wire fence, and plunges into a shallow pond. Marvin screams at both brothers, declaring their journey is over because he cannot stand them. He confesses that their father is dying, but wanted to hide the news from Buddy and Bobby. When Marvin cools down, they return to the road with a battered fender.
Near Miami, they stop at Tammy's house, but Buddy discovers she is living with a man named Rick (Ray Lykins). Tammy tells Buddy she thought she would never see him again. The brothers stop at Uncle Phil's house to borrow money to fix the Cadillac, but despite his expensive home, Phil is penniless because he gambles at the dog track. All he can give is a "hot tip" on a race. Marvin convinces Bobby to pawn his coin collection for $90.
That night, Buddy returns to Tammy's house with a bouquet of roses, while Marvin and Bobby go to the dog track. Studying a tout sheet, Marvin decides not to bet on Uncle Phil's tip but rather his own choice, and his dog wins. Meanwhile, Buddy makes love with Tammy and wants to rekindle their college romance. However, Rick comes home early and beats him up. The next morning, when Marvin hears what happened, he goes to Tammy's house and punches Rick in the face. Meanwhile, Fred Libner tests his plastic stop sign by replacing a city sign at a nearby intersection, but as soon as he leaves, wind blows it away.
The brothers take the Cadillac to Doc Sturgeon (James Gammon), a mechanic who works on vintage automobiles, but because of the their limited funds and 24 hour deadline, Sturgeon enlists them to do the work under his supervision. Tammy arrives at the garage and tells Buddy that Marvin broke Rick's nose. Bobby apologizes to Marvin for accusing him of not looking after his kid brothers. As Buddy and Tammy embrace, Marvin and Bobby hug. After they restore the Cadillac to pristine condition, the brothers drive toward their parents' home, but Rick and his friend, Raymond, intercept them. Fighting on the same side, Marvin, Buddy, and Bobby send the tough guys running. As the brothers get back in the Cadillac, an old man turns the corner too fast, because the stop sign is no longer there. The man hits the Cadillac's driver's side door.
When the brothers arrive home, their mother is happy to see them and loves the Cadillac. Their father notices the smashed door, but tells them he does not care. Setting up the journey was a ruse to force the brothers to deal with each other. Marvin admits to his father that he told Buddy and Bobby about his illness. As the family goes into the house, Fred says, "You did good, Marvin."