The first time Rudolf Serkin played in the United States, he recalled recently, was at the Library of Congress. Tonight he's back in Washington, this time as a recipient of one of the Kennedy Center Honors.

After finishing one of his daily rounds of practicing, Serkin reminisced in his suite at the Watergate Hotel about that first American concert: "It was in 1933 here in a Coolidge Festival. I came over with Adolf Busch and the Busch Quartet." By 1937, Serkin was back for good, along with his wife Irene, who is Busch's daughter.

Now 78, Serkin has long been acknowledged as one of the world's great musicians, a supreme pianist, a master of chamber music and one of the most sought-after teachers. It was with Busch that Serkin founded the music center at Marlboro, Vt., where each summer he teaches, coaches and plays. "The goal," he once said, "is to find the most gifted young musicians and hope they learn the difference between technique and art. We hope they will learn insights. Everyone learns, and everyone teaches." Something of the spirit of Marlboro is illustrated in the sign that greets those who enter its grounds: "Drive Carefully -- Musicians at Play."

Of the Kennedy Center Honor, Serkin said, with characteristic modesty, "I have read about it, but I never thought they would make it for me . . . I hope I do not have to speak -- I do not like to speak in public." When he was assured that the recipients of the honors are not asked to do a thing but be there, Serkin smiled broadly and said, "You make me feel happy."

Is Serkin, who will be 79 next March 28, planning any reduction in his busy schedule? Hardly. In addition to his customary round of orchestral appearances which this season will take him to Chicago, Philadelphia, San Francisco and Montreal, Serkin is in the midst of two major recording projects: He is completing a new set of the Beethoven concertos with the Boston Symphony Orchestra under Seiji Ozawa and a series of Mozart concertos with the London Symphony Orchestra under Claudio Abbado. There is also projected a recording with his friend Mstislav Rostropovich of the two cello sonatas of Brahms, to be completed in time for the 150th anniversary of the composer's birth in 1983.

The Kennedy Center award is the latest in a long list of distinguished honors that have been tendered Serkin during his half-century career. In 1963, President John F. Kennedy gave him the Presidential Medal of Freedom. He has played frequently at the White House. In addition to numerous honorary degrees from prestigious universities in this country, he has been decorated by foreign governments and honored by musical organizations including the New York Philharmonic, the Philadelphia Orchestra and the Academy of Saint Cecilia in Rome.

And what does the pianistic master think about all this recognition and adulation? "Sometimes," Serkin said once, "when you think you've played beautifully, they ask afterwards if you are all right. Then, when it's a mess, they say you've never played better in your life."