Washed-up actor Troy McClure gets pulled for driving without wearing his corrective lenses. When Troy goes to the DMV to get his license changed so that he will not be required to wear glasses anymore he offers to take Selma Bouvier to dinner if she will let him pass the eye test.
After dinner at the Pimento Grove, photographers notice Troy leaving with a human woman (rumors about a romantic abnormality initially destroyed Troy's career). The next day, Troy's agent calls and says that he can get work again if he continues seeing human women. Troy continues dating Selma to help his career. On his agent's advice, Troy asks Selma to marry him. Troy gets a part in 'Planet of the Apes' the musical.
The night before the wedding, a drunk Troy tells a drunk Homer the reason for his marriage and Homer goes wide-eyed. At the wedding, when Reverend Lovejoy asks anyone who opposes the marriage to speak up, Homer makes gibberish noises in his head to distract himself from saying the truth. After the wedding, Homer tells Marge offhand that Troy doesn't really love Selma and is just trying to aid his own career. Marge and Patty try to explain Selma, who accuses them of coming down with "the green-eyed gazungas." She confronts Troy who eagerly admits that their marriage is a sham to help his career. Troy explains to Selma that even though their marriage is a sham, she has benefited and Selma initially accepts the situation. Troy's agent thinks he can get Troy the part of McBain's sidekick in the next McBain movie, but most parts go to actors with families.
Troy and Selma try to conceive, but neither can get aroused. Selma decides that bringing a child into a loveless family is wrong and leaves Troy with the words "I'll always remember you Troy but not from your films." Troy turns down the role of McBain's sidekick to direct and star in his own film.