The late, great and inimitable Sir Thomas Beecham once asked, "Why do we in England engage at our concerts so many third-rate continental conductors when we have so many second-rate ones of our own?"

The question is one that bubbles to the surface in this country as one American orchestra after another signs up a conductor among whose qualifications seems to be one that he must not be an American. Take Cincinnati for example.

For seven brief years until his death in 1977, the greatly gifted young American Thomas Schippers brought honor to Cincinnati and its orchestra, improving its technical discipline and adding vitality to its repertorie.

Even before Schippers' tragic death from cancer at 47, the names of possible successors to his prestigious post as the head of one of the top American orchestras were being murmures quietly or loudly by players, board members and interested bystanders. Like most orchestra players, those in Cincinnati were asked to fill out forms evaluating every guest conductor who led them in concerts. Those forms checked for opinions on: Baton technique, knowledge of the score, knowledge of the orchestra in front of him, musical style, rehearsal technique, leadership, re-engagement -- would you like him back again? -- and subjective response -- did you like him as a person?

"What the local musicans have to say could determine who gets the big job with CSO," wrote James Wierzbicki of The Cincinnati Post.

A search committee also was set up, with department-store owner Samuel Pogue as its chairman. According to David Joseph, head of the committee prior to his becoming president of the orchestra board, five characteristics were sought in the new director: A thorough grouding in music, a man recognized as superior by the musical community throughout the world; total dedication to music and the Cincinnati orchestra, one willing to work with the orchestra regularly, rather than as a visitor; a family man who has indicated he wants to settle in Cincinnati; a practical administrator who also has earned a reputation for flexibility in dealing with people; and a musician with a reputation for versatility to please the music-goers of Cincinnati.

Both sets of criteria proved to be window dressing when, on Dec. 21, 1978, it was announced that Michael had been named music director.

Gielen, who is 53, was born in Dresden, Germany. He is music director of the Frankfurt Opera and principal guest conductor of the BBC Symphony in London. He is best known for conducting avantgarde music of recent years, and in the Schoenberg, Bartok and Stravinsky repertore. In a BBC Symphony concert on Feb. 13, his program was of Stravinsky, Zimmermann, Goehr and Webern.

Gielen had never conducted the Cincinnati Orchestra, is completely unknown to the players in the orchestra and was unknown to the board of directors, who were excluded from any say in choosing him.

His guest appearances in this country, which date back to his debut with the New York Philharmonic in 1971, have included concerts with the Chicago, Pittsburgh, Minnesota, Detroit and National Symphonies. With the National Symphony, Gielen conducted in the 1972 Mozart Festival; in the Festival of the Old and the New in 1974, he led works by Stravinsky, Penderecki, Haubenstock-Ramati, Copland, Ligeti and Zimmermann.

Questions are now being raised in Cincinnati not only about the unknown Gielen but about the whole process by which he was chosen and the orchestra ignored. The unbelievably naive statement announcing Gielen's appointment stressed that "the committee learned that among other things, Gielen was totally dedicated to music and worked at it year round and that one of his favorite forms of recreation was to study scores." It is hard to think of a single decent conductor of whom this is not true.

As for ignoring orchestra musicians, this is an old device when it comes to choosing conductors. The members of the Cleveland Orchestra were polled on Istvan Kertesz and Lorin Maazel as a successor to George Szell. They were nearly unanimously for Kertesz and Against Maazel, but the boare picked Maazel.

A different situation is brewing in Philadelphia where Eugene Ormandy holds a contract "for life." But he will be 80 next November, and it is inevitable that, while he may remain as music director and continue to conduct each season, a successor for his extremely desirable post is in the highly visible stage.

The man whom Ormandy himself has called "a natural" is Riccardo Muti, who already holds the unprecedented -- for Philadelphia at least -- title of Principal Guest Conductor. He is also presently director of the Maggio Musicale in Florence, Italy, and a principal conductor of the London Philharmonia.

On the basis of various Muti-Philadelphia concerts here, and in numerous recordings, including one of "Aida," Muti has consistently sounded rather superficial, a man who glides smoothly over the profound slow movement of the Schumann Second Symphony, races through the grand moments in Verdi's opera, and in general tends to take an easy, glamorous route. In Philadelphia, some close to the orchestra say, with a strange kind of pride, "Ah, the ladies love him so!"

The question that continues to force itself to the front these days is this, with a backward look at Sir Tomas's needling query: Why not place at the head of the list of qualifications for a new conductor of an American orchestra, "He shall be an American."

The Metropolitan Opera has shown an admirable desire to find and exploit telented young American conductors. So have the opera companies of Boston, Dallas, Seattle, Santa Fe and may other citles. So, too, have most U.S. orchestras.

It is only a weird kind of snobbishness carried over from previous generations that continues to place an Indian at the head of the New York Philharmonic, a Japanese in Boston, a Romanian in Baltimore, a Hungarian in Chicago, a Mexican in Dallas, a Dutchman in San Francisco, an Italian in Los Angeles, an Englishman in Minneqpolis and a Russian in Washington, unless these men have clearly proven virtues not to be found among the conductors of this country. The excellence of American conductors, which gave Cincinnati's orchestra new prestige under Schippers' direction, can be heard these days in Cleveland, Pittsburgh, Houston, Buffalo, St. Louis, Salt Lake City, Kansas City and any place where Leonard Bernstein conducts. Meanwhile, Cincinnati and Philadelphia deserve what they seem likely to get.