Ballet student Julie Cox, 16, of Potomac, was one of four scholarship award winners in the Prix de Lausanne in Switzerland this weekend, the only American dancer to win a prize in the prestigious international competition.

Cox, who returned to Washington last night, said she found the experience very enlightening. '"I had a very good time, but it was also very hard work. The competition was a lot harder than I thought it would be. It started with 85 dancers, and it was an achievement even to make it to the second round. It was interesting to see how many very good dancers there are in other countries."

*Cox was given one of four equal awards, each of which includes a medal and a year's tuition at a leading ballet school (in the United States, the designated schools include the New York City Ballet's School of American Ballet). She also was the only one of nine American dancers entered in the contest to reach the final round.

Winner of the competition's top gold medal was Gregor Zeiffert of East Germany. Several other prizes were awarded in other categories.

Cox lives with her parents, Charles and Jennifer Cox, and studies with Tensia Fonseca and Michelle Lees at Fonseca's Academy of the Maryland Youth Ballet in Bethesda. Among former students of the same school are Susan Jaffe, Peter Fonseca and Cheryl Yeager, all now members of American Ballet Theatre.

The Prix de Lausanne, one of the half dozen most highly regarded ballet competitions in the world, has run annually since 1973.

*Cox is scheduled to dance featured roles, including Aurora in Act III of "Sleeping Beauty" in four performances by the Maryland Youth Ballet Feb. 21 to 23 at the University of the District of Columbia Auditorium. After an audition with Mikhail Baryshnikov, Cox was chosen to appear as an apprentice with ABT in "The Nutcracker" performances in Los Angeles in December. Last summer, as a scholarship student at the School of American Ballet, she was chosen to dance in the school's Choreographer's Showcase at Lincoln Center's Juilliard Theater. Last spring she was awarded a first prize of $2,000 in regional finals of the National Society of Arts and Letters competition, held at the Kennedy Center.