Alex Olmedo, the Peruvian who dominated the world of international tennis in 1959 when he won the Australian and Wimbledon men’s single championships and reached the final of the United States Nationals at Forest Hills, died on Wednesday in Santa Monica, Calif. He was 84.

The International Tennis Hall of Fame in Newport, R.I., said the cause was brain cancer. Olmedo was inducted into the hall in 1987.

Olmedo took his first steps toward tennis acclaim at the club in Arequipa, Peru, where his father, Salvador, who oversaw the courts, gave him pointers. He was also guided by Stanley Singer, an American tennis coach working in Peru. He made his major championship debut in 1951 when he was 15, losing in a preliminary round at Forest Hills.

After settling in the Los Angeles area, he was coached at the Los Angeles Tennis Club. Playing for the University of Southern California, he won the N.C.A.A. singles and doubles championships in 1956 and 1958.

Olmedo won his two singles matches and a doubles match, teaming with Ham Richardson, to lead the United States to victory over a strong Australian team in the 1958 Davis Cup final, at Brisbane.

His selection for the American squad proved controversial, since he was not a United States citizen. But regulations permitted a player to compete for a country after at least three years of continued residence. And Peru did not have its own entry in Davis Cup play.

Allison Danzig, the longtime tennis writer for The New York Times, wrote that Olmedo’s selection showed that U.S. tennis authorities gave “equal opportunity to every player, to the foreign born as well as the homebred.” But Arthur Daley wrote in his column, Sports of The Times, that Olmedo’s participation “has to make American tennis the laughingstock of the rest of the world.”

Don Budge, the 1938 Grand Slam champion, responding to a Sports Illustrated survey of sentiment among leading tennis figures, wrote: “Selecting Olmedo isn’t saying there is something wrong with our tennis. However, we should stimulate more interest here to match Australia’s.”

Olmedo, who held a student visa while playing for U.S.C., said that if he decided to remain in the country permanently he would become a citizen. He did, many years later.

Late in the 1958 season, Olmedo teamed with Richardson to win the men’s doubles title at Forest Hills.

Olmedo was at his best on fast surfaces, where he could display his quickness and forge an aggressive game.

His extraordinary 1959 season began when he defeated Neale Fraser of Australia in four sets for the Australian championship. He downed another Australian, Rod Laver, who at the time was only 20 years old and unseeded, in straight sets in the Wimbledon final, adding lobs to his customary serve-and-volley game along with strong groundstrokes.

Olmedo lost to Fraser in the Forest Hills singles final.

After only two seasons as an amateur (and long before the Open era, when professionals were allowed to compete alongside amateurs), Olmedo joined Jack Kramer’s touring pro circuit. He defeated Tony Trabert for the 1960 U.S. Pro Tennis title.

Olmedo retired from competitive play in the mid-1960s. He was a longtime teaching pro at the Beverly Hills Hotel, a magnet for Hollywood stars, where his pupils included Katharine Hepburn and Robert Duvall.

Alejandro Olmedo was born on March 24, 1936, in Arequipa. His survivors include his son, Alejandro Jr.; two daughters, Amy and Angela; and four grandchildren. His marriage to Ann Olmedo ended in divorce.

Olmedo was the second International Tennis Hall of Fame inductee to die in recent days. Dennis Ralston, also a star at U.S.C. and a five-time doubles champion in majors, died on Dec. 6 in Austin, Texas.

While honing his skills at the Los Angeles Tennis Club, Olmedo received pointers from George Toley, the club’s head pro and the coach of the U.S.C. tennis team.

But above all, he was confident in his own instincts and court savvy.

“I have a philosophy,” he told Sports Illustrated in September 1959. “I have heard so much from so many. I never listen exactly. I mean, I listen, but I don’t. I learn most from the players I play against. That’s the big way you learn tennis.”