The press agent, who's paid to say such things, is saying that Matthew Broderick is on the cusp of stardom.

All it will take is for "WarGames" to hit the nation's movie screens, an event scheduled for June 3. He's touting the film, since he is paid for such toutings, as "The China Syndrome" of 1983, when he's not selling it as the one summer release likely to hold it own against "Return of the Jedi."

There's is no way, he's insisting, that Master Broderick -- playing a high school computer buff who inadvertently taps into the country's defense system in Colorado, and very nearly triggers World War III -- can't also charm his way into the country's heart.

Except that Broderick, scheduled to give an interview at 1 p.m. at the Alvin Theatre, is nowhere in sight. It's already 1:15 and the press agent is getting nervous.

"Believe me, none of this has gone to his head," he says apologetically, after a quick call to check up on Broderick's whereabouts. "He's remarkably unaffected by everything that's happened to him. He still rides his bicycle to and from the theater. He plays softball in Central Park with his friends. He's not doing this on purpose. He's just a kid.He's only 21. I guarantee you he'll be here at 4."

It isn't until 4:35, however, that Broderick ambles down 52nd Street, by which time the press agent, a nailbiter, already has begun working on his knuckles.

Broderick has a hangdog look on his face, large brown cookie-jar eyes and a downy shadow on his upper lip. His hair is tousled and he looks about 15. He stares down at his feet, and then says, sheepishly, "Boy, you must hate me a lot."

If he were anyone else, you'd say, "You bet your sweat socks!"

But Broderick could easily be your kid brother, and what do you say to your kid brother when he's ripped your best sports jacket or stolen your razor and then stands there, tugging at his sweat shirt as if it were made of hair? You say, "Forget it, pal." And you do.

Talk about unilateral disarmament. This kid's got a gift, all right.

The critics already have cheered him as the teen-age son suddenly drowned in the largess of a long-lost grandfather in "Max Dugan Returns." They cheered again for his performance as Neil Simon's 15-year-old, sex-starved alter ego in the Broadway comedy "Brighten Beach Memoirs." Earlier this month, they put him up for a Tony award.

A press agent's words are borne out, for once. Broderick turns out to be refreshingly level-headed about the success that has come up, like thunder, out of the flat landscape of auditions, call backs, and thanks-but-no-thanks that is inhabited by most stuggling New York actors. "All this time, you keep thinking, "If I could just get that job, things would be fine,' And then you get the job and it's still not fine," he says. "I used to wonder what it would be like to see my name on a billboard. I couldn't even imagine something like that. Then you see it and well, it just makes billboards not as special as they used to be. It's weird."

"A lot of people resent what's happened to me. They think it's such a luck-out, which it is in a way. People don't come right out and say it, but I get a lot of fake smiles, especially from actors. Friends of the family, who haven't had a job in 15 years, blame me because they're out of work. I can understand that . . . a little. I feel bad for them. But it's not my fault that this is the way the world is organized -- that people in a hit show of a hit movie get all this attention and money. I didn't design all that. They're mad at me for something I have no control over. I just try to do my best."

He flops down on a ratty couch in the theater's green room, nodding casually to the various cast members of "Brighton Beach" who wander through in the course of the interview.

"My father warned me it would be like this. When he did that TV series, 'Family,' he thought, Great. I'll make enough money to pay off the house and keep the family together, but I'll probably lose some friends.' And he did. It's ture -- a lot of people can't handle your success."

Broderick's father was the highly regarded actor James Broderick, and the dark side to the meteoric rise of Matthew Broderick is that is coincided with the lingering illness of his father, who died of cancer at 55 in New York on Nov. 1, 1982 -- the very day that his son began rehearsals in Los Angeles for "Brighton Beach Memoirs."

Broderick speculates that he probably became an actor in the first place because of his father. Watching all those years from the wings, he absorbed both his father's gift and enthusiasm for acting. The two managed to appear together only once -- in Horton Foote's "Valantine's Day" for a 12-performance run in New York. "I played his son in military school -- a total f--- up." Broderick recalls. "There were a couple of instances when we'd both be reading for the same TV movie. I remember one. He took the part, thinking I was going to get cast, too. Only he didn't tell me. What he wanted was for me to come on the set for this scene between a businessman and a kid, and there he would be. But I didn't get the part. He was infuriated."

The son's luck changed, although it didn't appear to be much of a breakthrough at first, when he landed in Harvey Fierstein's "Torch Song Triology," as a bright gay teen-ager who is adopted by a drag queen. "Torch Song Trilogy" then was far from being the Tony-nominated Broadway hit it is now. "Not that many people even read for the part. Everybody wanted to stay away from this weird, gay play. I had an agent who didn't even think I should do it," admits Broderick. "We were playing in this sleazy walk-up theater on the fourth floor with columns everywhere. I loved the play, but I thought 'Nobody's going to come see this.'"

Nobody did, until the New York Times gave the show an unexpected rave. Their curisoity piqued, other critics dropped in. Before long, "Torch Song" had moved to a respectable off-Broadway theater and was a flouncing success. In one of those chain reactions in which the theater sometimes resembles nuclear fission, Broderick 1) auditioned for and won a leading role in "Brighton Beach Memoirs," the autobiographical comedy by Neil Simon, who 2) decided that first he would put Broderick in his new movie, "Max Dugan Returns," the early rushes of which were seen by 3) producer Leonard Goldberg, who concluded he wanted Broderick, too, for "WarGames."

Broderick gave one last performance in "Torch Song," caught the 7:30 a.m. plane to Los Angeles, arrived by 9, and was rehearsing on the set that afternoon. Barely 20, he found himself caught up in "this wild beat-the-clock contest," -- getting through "Max Dugan" in time to film "WarGames" in time to go into rehearsals for "Brighton Beach." Meanwhile, his father was dying.

"I'd get in these big panics during the filming of "Max Dugan,'" Broderick recalls. "I had all these scenes where I'd have to discover these gifts that Max (Jason Robards) keeps giving his daughter and grandson. It used to scare me. I'd say, 'Oh no, tomorrow they're going to pick me up at 7:30 and I'm going to have to see this Mercedes-Benz, and go 'hooray.' That was hard for me, I don't know why. I remember calling my father and saying, 'What do I do? How do I get excited and not anticipate things?' 'Don't think about it,' he'd say. You'll get excited when the time comes.' He was very good at calming me down. 'Stay loose' was a big piece of advice with him.

"Jason was very helpful to me at that period of my life, too. He knew my dad, and he'd always ask me how that was going. We ate a lot together and he'd crack me up on the set. I realized that his jokes were almost his preparation for Max Dugan. You never knew what he was going to do. It was a very spontaneous way to work."

By the time "WarGames" went before the cameras, the situation at home was critical and Broderick was flying back to New York every weekend to be at his father's bedside. "Some people say acting is a kind of therapy," he reflects. "It didn't seem to help me. Doing 'WarGames' was like time out. On the set, I'd forget the tragedy that was happening at home. But whenever I'd come home from shooting, it was just as horrible as it had been the weekend before. It was just like these . . . two different times."

Shooting on "WarGames" fell behind schedule and ran over into the first days of rehearsal for "Brighton Beach." Broderick was spinning faster than ever. "My father wanted me to phone him after the first reading of the play and tell him how it had gone. I did and he asked a lot of questions," Broderick remembers. "He died that very night. I can talk about it now, but when I was younger, 16 or so, I was always afraid he'd get sick and die. It was the one thing I thought I couldn't take. If it had happened any earlier than it did, I wouldn't have gotten through it. It's funny. If he were alive today, the two of us could pretty much do what we wanted. We could pick a play . . . " His voice drifts off.

If Broderick's career seems to argue for the existence of magic wands, it also seems to illustrate the truism that actors are indeed born, not made. He admits to being the class clown at Walden School in Manhatten, appeared in high school plays, and studied briefly with Uta Hagen. But he's both modest and, one gathers, healthily unaware of the wellsprings of his talent, the ingrained sense of comic timing and the sly irony he projects without being wise-ass. The only explanation he has is that he must have learned how to act "by omosis."

"My father had a really fine technique," he says. "Oh, he blew it occasionally. But he could really take almost any part and be completely different. He didn't rely on any quality he had. I like actors who are sort of different and eccentric -- not what you expect.I like somebody who takes chances -- Jason; Harvey Fierstein, who has the guts to bare all; Peter Sellers, a real genius. I saw Al Pacino on the street once. That made me very nervous. I think if ever I met Peter O'Toole, I'd faint."

On the stage and screen, Broderick registers younger than he looks by four or five years, which makes him a potential idol of the country's youth, a marketing possibility that already has occurred to more than one Hollywood mogul. "The kid in 'WarGames' is the oldest I've played yet. He's 17 and he's beginning to be interested in girls, which is new. Oh, my character in 'Brighton Beach Memoirs' is interested, but he's at a total loss as to what to do about it. In 'WarGames,' the character has a girlfriend and he kisses her at one point. That was fun. It took quite a few takes. After we finished the scene, I just sort of expected to keep on kissing her. But she wasn't interested at all. I had a little trouble cutting it off."

Broderick, who recently extended his contract in "Brighton Beach Memoirs," faces the prospect of six more months of nightly performances with equanimity.But he still gets nerous when he sees himself on the screen. "When I saw 'Max Dugan' for the first time, it was terrifying. I had someone feel my chest and it was beating THUMP,- THUMP, THUMP. I was gone. You get these weird angles, which is kind of neat. I mean, I never realized what the backs of my arms look like. But I get very vain. Fifty percent of me is thinking, 'Am I any good in this part?' But the other fifty percent is thinking, 'How do I look?' I enjoyed 'Max Dugan,' but I thought my hair looked pretty bad."

He continues to live in Greenwich Village with his mother, Patsy, who reads the scripts that are coming his way -- in stacks -- and offers her advice. For the time being, he keeps his money in a checking account. "I'm f------ up terribly," he says. "I'm gonna have to get somebody to handle it." The only indulgence he allows himself so far is to take his friends out to dinner, order a good bottle of wine and not fret about the tab.

But the rumble of fame is growing louder. "I've begun to get letters from girls 18 or so, who think I'm 15, and want to know if they and their mothers can take me out to lunch. And the weird calls have started. The other day, someone called me and said, 'Hello, Matthew, I'm your sex goddess.' I guess I'm going to have to change my number.I'm still a little in awe at what's happening. It just seems to snowball into this big deal. I can't believe the numbers. Every night, 1,300 people are seeing me in the theater. I like that, but I can't quite conceive it. And when you talk about the films . . . well, I get letters from people in Wyoming who liked 'Max Dugan' and I have never been to Wyoming in my life."

If it's already this way for Broderick, what's it like for Brooke Shields?

"It must be horrifying," he says. "She's not only more famous than I am, she's prettier. She's also smarter."

He cracks a sly grin. "If I called her up and asked her for a date, she probably wouldn'a a heard of me."

His eyes twinkle. "But I could try . . . Maybe, I could write a letter."