John Nelson, who conducted the Indianapolis Symphony Orchestra Saturday night at the Kennedy Center, is a rare specimen -- not only because he is the American-born conductor of a major American orchestra.

"There aren't many of us," Nelson said in a recent conversation, "or rather not many in the top positions. Young American conductors are out there in abundance. I've begun noticing how many there are and how good they are since I've been looking for an assistant conductor. There have been more than 300 applications, and I'm bringing some of them in for auditions."

Nelson is not critical of the conductors from Europe who direct the orchestras in Philadelphia, Washington, Chicago, Detroit, Los Angeles, San Francisco and Minneapolis, the conductor from India who directs the New York Philharmonic, or the Japanese conductor of the Boston Symphony. But he wonders why there are not more major orchestras like the Cleveland, which has an American music director. (Lorin Maazel is an American citizen, though he happened to be born in France and does much of his work now in Vienna -- like that other American, Leonard Bernstein.)

"I think American conductors need to take the reins," he says, "because we relate to and understand the American culture. Foreign conductors do not really understand an American women's committee, the financing of American orchestras, or American audiences."

Now in his fourth year with Indianapolis, Nelson, 38, has taken his orchestra on several tours and received widespread critical acclaim in cities where critics are not notably easy to please. The orchestra has been called "splendid sounding" in Chicago, where the resident orchestra is specially noted for splendid sound. Its Berlioz Requiem was found "absolutely magnificent" on a previous visit to Washington, and it was credited with a "first-class performance" in New York.

Nelson has made a special reputation as a conductor of large, complex works involving chorus and orchestra -- works like Mahler's Second Symphony, which he conducted here last week. He first won special attention, shortly before taking his post in Indianapolis, when he substituted for the ailing Rafael Kubelik at the last minute, conducting a Metropolitan Opera production of Berlioz's "Les Troyens." Besides performing the "Requiem" here with his own orchestra, he conducted the National Symphony in it when Mstislav Rostropovich was stricken ill.

European conductors do have some advantages over Americans in what is still basically a European repertoire, Nelson believes: "My question about young American conductors does not concern their abundance or their technique; I wonder about the depth of quality in all of us, not excluding myself. The teaching is so good in Europe, the cultural roots are so deep. Riccardo Muti likes to go back to Italy periodically, just to walk through the streets where Donizetti and Rossini walked, and he brings some of that back with him.

"This breadth of culture is what I find lacking in American musicians. If I had my training to do over, I would start to work at being a conductor when I was 15 -- I had no idea that this would be my life when I was that age -- and I would spend a great deal of my time in Europe."

During his four seasons in Indianapolis, Nelson believes, he has gradually built an audience "more attuned to the music-making than to a personality." He recalls guest-conducting the orchestra in November, 1975, to an audience of 650 in a 2,200-seat hall. "Now," he says proudly, "the entire season is sold out by subscription; it is a young, enthusiastic audience, and I find that it responds warmly to music that is not familiar -- like Shostakovich's 15th Symphony -- if it is good and well done." The orchestra has a budget of $4 million, about 30 to 40 percent of which is derived from ticket sales; it has 86 regular players ("heading for 96," Nelson says) and plays a 46-week season ("heading for 52").

The Indianapolis metropolitan area has a population of about 1.2 million (less than half of the Washington metropolitan area), and Nelson says, "I like to think we have the best orchestra in the country for the size of our area."

The size is, nonetheless, a limiting factor, and when he is asked about his plans for the future, he admits that "there are limits to the growth possibilities of an orchestra in an area this size."

But he adds immediately that he is not feeling restless and has no plans for moving on. "There is still plenty for me to do in Indianapolis," he says.