Desi Arnaz Jr. in ''The Mambo Kings''

He doesn’t consider himself an actor. Then again, says the son of Lucille Ball and Desi Arnaz, ”I wouldn’t say I’m not an actor, either.” Well, it’s safe to say he does act: Desi Arnaz Jr., 38, plays his own father in The Mambo Kings, the story of two Cuban brothers invited by Desi Sr., an immigrant who is the American dream incarnate, to appear on his TV show.

When director Arne Glimcher first proposed the casting three years ago, Arnaz says, ”My mother had just died, and I didn’t feel the timing was right.” Last year Glimcher visited Arnaz at his home in Boulder City, Nev., and asked him again. ”He said he’d seen a lot of people who could impersonate Ricky (Ricardo),” says Arnaz, referring to his father’s I Love Lucy character, ”but nobody who knew who Desi was.” So he read Oscar Hijuelos’ novel, liked it, and signed on.

Arnaz dyed his graying hair black-as his father had-for his role as Ricky, and wore an ID bracelet, ring, and pin that belonged to his dad, who died in 1986. ”I wasn’t trying to look exactly like him,” says Arnaz, whose brown eyes and sightly impish smile nonetheless do. ”It was more about getting his essence and mannerisms.”

Arnaz has worked even harder to find himself. After making a splash in the ’60s with the teenage rock band Dino, Desi and Billy (along with Dean Martin Jr. and Billy Hinsche), he fell into the fast life of celebrity dating (Liza Minnelli, Patty Duke), drinking, and drug-taking. By his mid-20s, he was in a recovery program. Four years later, he helped Desi Sr., then 66, go through the program himself. ”We got to say everything we ever wanted to say, as a father or as a son,” recalls Arnaz.

Married since 1987 to Amy Bargiel, a dance teacher, and the adoptive father of Amy’s 14-year-old daughter, Haley, Arnaz is national spokesman for the New Life Foundation, a nonprofit group organized by self-help guru and author Vernon Howard. ”I guess I’m a student of spiritual development,” he says. That, and the second generation of the American dream.