Donna Coleman was No. 2. And perhaps it is no coincidence that she tries harder.

"I went to hear Brad Gowen play on Wednesday night, and I knew he was going to win," pianist Coleman remarked during the final round of the first annual Kennedy Center-Rockeffer Foundation International Competition. She was right on target.

Sunday afternoon, Gowen strode on stage in the Kennedy Center Concert Hall and played a dazzling program that won him a clearly well-earned $10,000 first prize.

He seemed totally cool until composer Leon Kirchner announced his victory; then he became intensely nervous.His face paled under the luxuriant black mustache and his expression was one of shock. It was replaced by a big smile when Donna Coleman, seated in the next chair, reached over to give him a congratulatory hug, which seemed to make it all official.

The hundreds of big-money music competitions (in which the Kennedy Center-Rockefeller is the latest entry) sometimes make you think that music is like a horse race. Last June, this contest, which focuses on contemporary American music, had 89 participants. A week ago, there were a dozen, and by Saturday afternoon there were only three.

"It's fairly easy to weed out the bad pianists," said finalist Robert Weirich, who eventually finished third, "and there's not too much trouble with the mediocre ones - but when you get down to three finalists at this level, it's like choosing between apples and oranges."

The big apple of the contest, Bethesda native Gowen had the special thrill of winning and international competition in his hometown while a legion of friends, former teachers, both parents, both grandmothers, an aunt and his wife (and fellow painist) Maribeth led the audience in wild applause.

"It felt normal to be preparing to perform, and if felt normal to be going to the Kennedy Center," he mused, "but the relationship between the two activities kind of flabber-gasted me."

Gowen already felt like a winner 24 hours before his first prize was announced, when he knew he would be a finalist. "At the beginning, any little thing can make you feel insecure," he said, "but now the pressure is off. I have won a chance to play a Kennedy Center recital and a check will come for some unknown amount." The first prize also includes performances in 35 other cities of the United States and Canada.

In an interview, Gowen, 32, seems more cautions, less self-assured than in front of a piano, where he is a complete master of the situation. He fretsand hesitates when asked to classify the music he doesn't like.

In contrast, runner-up Coleman, who is 26 and just out of the Easyman School of Music in Rochester, bubbles with enthusiasm and doesn't hesitate to declare that the First Piano Sonata of Charles Ives is "as delicious as a chocolate eclair. "Diffident about her technique, which she began learning at age 5 from a church organist in her native Philadephia, she seemed amazed at winning a $5,000 second prize (which is higher than the first prize in most music competitions).

"If I applied for the Juilliard or the Curtis tomorrow," she said, "I probably couldn't pass the entrance examination."

She said that she enters few competitions because she is "scared to death of them and anyway they don't really relate to music.

"I have a very personal style, and I'm not sure how other people will like it. I listen to other pianists and I think they're sensational and I can't match them technically, so I just go back and try to perfect my own style. It's very reassuring to know what I can do so well in this kind of competition, because . . . well . . . you don't want to go out on the stage and worry that people will throw tomatoes at you."

"I love to play for audiences, but I have this self-doubt syndrome-I suppose every sensitive person has that every day. I have something to say and I want people to hear it, but I worry terribly that they won't like it, and that's myself that I'm pouring into the music.

"I hesitated and waited until the last minute before entering this contest, but I had to do it because if was my kind of music they wanted to hear. I told myself, They'll disqualify me and I'll feel terrible and want to give up music,' but I forced myself into it."

Though she has been interested in music since she was 5 years old. "I wasn't seriously involved in it until I went away to college; as a kid, I really preferred playing in the mud the practicing."

Just finished with her doctoral studies ad "just beginning to get my act together," Coleman had begun her first teaching job at East Carolina University. (I've only been there two weeks, and I'm taking all this time off; I hope they don't fire me.") She is still trying to choose between an academic career, the life of a traveling artist, or the uneasy combination of the two, for which most solo musicians settle nowadays.

"I play wherever I can, but I'm not very experienced and would like to find out more about what it involves," she said. "I decided a long time ago that I would have to be a teacher for the security it offers and use that as a base of operations before I start pushing myself out into concert life."

Gowen and Weirich are already established in universities-Gowen at Alabama, Weirich at Tulane-and have also gone further on the performance circuit.

Gowen will begin his third organized concert tour next month, chiefly in the Midwest, where he has found small-town audiences surprisingly open to modern music.

The 28-year-old Weirich (whose third prize was a healthy $3,000 while the nine semifinalists each received $1,500) gave 25 public performances during the past season. Besides his solo work and an active involvement in New Orleans chamber music, he is soprano Phyllis Curtins' accompanist.

But neither man feels that he has experienced the kind of the life that is routine for the peripatetic virtuoso, living largely on jet planes and in hotel rooms. That life is hotly criticized among musicians, but all three finalist felt in Gowen's words that they would "like to try it, if only to have enough experience to say I don't like it."

There was a small taste of that life after Leon Kirchner announced the winners and handed them each an envelope.

Kennedy Center executive director Martin Feinstein, who gave each of the winners a small bust of John F. Kennedy, announced that they were in a hurry to get to the White House for the recital being given there by Mistislav Rostropovich, but enthusiastic members of the audience swarned on stage and engulfed the contestants.

It was a long time before Gowen could tear himself loose and run up the aisle-stopping repeatedly to shake hands and say "Thank you"-to hug his aunt and grandmother, and more than half an hour before the winnes could form a bedraggled cavalcade to dash off to 1600 Pennsylvania Ave.