Mariel Hemingway, the toast both of Woody Allen's "Manhattan" and the island it romanticizes, is bouncing up and down on the trampoline in the back yard of her parents' ranch-style house.

"We were going to get rid of it," says her mother, Puck, eyeing the gym equipment on which her teen-ager bounds and rebounds. "But look, she's using it again."

Mariel, back from the Cannes film festival where she went with her father, Jack, to represent the cast of the movie, has just returned from a trip on a private jet to Hollywood, accompanied by her parents, to talk about another movie part.

Will she do it? "I don't know yet," Mariel replies in her little-girl voice.

At 17, however, she does know that she wants to make more movies; doesn't want to model "because I don't like it"; and "probably would like to do things that are different" from her role as a precocious 17-year-old who is having a grown-up love affair with the 42-year-old writer played by Allen in "Manhattan."

As for whether the movie role reflects any of her own experience - the very notion startles her. "Of course not. I'm not like that."

Susan Cook, a longtime family friend, declares Mariel "an Idaho innocent, just like Margaux was when she went to New York. I haven't ever seen her date boys. When she comes home she goes out with her friends. She's not spoiled at all. And she's not demanding."

Some of her friends here do think Mariel has changed. Says Stephanie Shumway: "She and I used to be very close, but she's sort of cut us out a little bit. I don't think she doesn't like us. I think she thinks we don't like her. But that's not true. Everybody likes her a lot."

Mariel had spoken of an interest in marine biology, but wound up making her movie debut at 14 in "Lipstick," in which she and her sister Margaux both played the part of rape victims. Mariel caught Woody Allen's eye, though in her next project she was cast as an unwed teenager mother in the TV movie "I Want to Keep My Baby."

Last year her agent told her that Woody Allen wanted to meet her - and he offered her the role of his adolescent lover in his new movie. "Manhattan" was warmly received by critics, and Mariel's contribution cited as an effective foil to the citified Allen style.

The Hemingway girls often come home to this little town, just outside of Sun Valley in the Sawtooth mountains where their legendary grandfather, Ernest, spent the last years of his life. They are a very close-knit family, very respectful of their parents.

They've never been in any real trouble," says Cook. "They're very good to their mother," who is extremely protective of them and their privacy. The unassuming house, just north of Ketchum, has no name on the mailbox, which helps keep away gawkers. Even the local taxi driver isn't sure where it is.

Margaux, model and actress, who at 6 feet is 2 inches taller than Mariel and seven years older, was home last week, too, with her fiance, French-born Venezuelan film director Bernardo Foucher. Muffet, 29, had just left for a European tour with her godmother. All of them live in New York, including Mariel who shares a Greenwich Village apartment with her best friend from Ketchum, Sara Mylerberg, a 10-speed bike and a cat.

"It's ironic, I suppose," says Cook, "that she has an apartment in New York at 17. But one reason I think she is able to is because of the security her family gave her. And in a pinch she can call on her sisters, or Bernardo or Woody. She and Woody have become good friends."

Mariel is quite protective of Allen. Her tentative young voice becomes quite firm when she says. "No, he's not neurotic. He's brilliant. It was fun working with him. I'd like to do it again."

But when her mother says Allen, whom she "adores" and who is her "favorite actor" had pinned a note on the refrigerator door when he visited briefly last year, Mariel disagrees. "No it wasn't, Mother. I put it there."

The note is directed to a house full of dieters: "Standing before the refrigerator, if I have to ask myself if I'm hungry, I'm not."

Mariel, a vegetarian, who used to jog and ski when she lived in Ketchum, is trying to get her father to go on a vegetarian diet so he can lose the five pounds he put on in France. Margaux is on the Scarsdale diet. Only Puck doesn't have to count calories.

Everyone is in the small kitchen, cooking at the same time. The five-pound Yorkshire terrier, Macko, short for Mack the Knife, is sitting on the kitchen counter, sniffing the wine. Mariel and her father exchange words briefly over who is in whose way.

"Don't do that, Daddy," she says.

"Well, get out of the way," he responds as he stirs the court bouillon.

The next day she and her sister are to take a fly casting lesson from her father's fishing buddy and professional guide, Bill Mason. "If they're good at it, I'd like to take them fishing with me," says Papa Hemingway's first son, who is an expert.

Then Mariel, who was named for a bay in Cuba where her parents once picnicked, was off to party with some friends during graduation week. She was to have graduated from private school next year, but left in the 11th grade to pursue her acting career.

"She's a natural," says Cook. "Last year she had the lead in the school play. I think even if she had been someone by the name of Smith or Jones she would have been a big talent."

Shumway says "some people think it's because of her name, but we think she's very talented."

Mariel Hemingway seems just like most young, shy girls from small towns. She hasn't spent much time dwelling on the cosmic significiance of the things in which she is involved, or of the effect of her artless charm.

It has not occurred to her that she is the toast of Manhattan because she portrays anti-Manhattan virtues in the film. "I'm kind or right in the middle of it without seeing it," she says.

The other characters in "Manhattan" are neurotic and brittle; she speaks the simple truth with a certain eloquence and directness.

"What's six months if we still love each other?" she asks her lover just prior to leaving for London in one of the film's most sentimental scenes.

But Mariel says she "has never thought" about her role as representative of old-fashioned simple values - and certainly has never made a connection between what she stands for in "Manhattan" and what her grandfather was saying in his books.

"Besides," she says, "That's not what the movie is saying. Old-fashioned virtues don't win out in life."

What is the movie about?

"It's explaining . . . I don't know," she apologizes. "I'm tongue-tied. It's too early in the morning."

"Manhattan" was shown at the Cannes Film Festival, and Mariel was there. She got to use her French, and dine at the three-star Moulin de Mougins. But by all accounts, Mariel was bored.

Last seen, she was sitting on the floor at the foot of her mother's bed, watching television. CAPTION: Picture 1, Mariel Hemingway sipping an ice cream soda in a scene from "Manhattan." Picture 2, From left, Mariel, Puck, Margaux and Jack Hemingway behind their house in Ketchum, Idaho. By Susan Snyder Cook for The Washington Post.