Claudio Abbado, at 45, is a high flier on the music scene. Few other conductors -- if any -- have so many performing institutions at their immediate beck and call. But Abbado had never before led the National Symphony.

"I conducted here before, with Philadelphia, with Cleveland and, of course, La Scala. But never with this orchestra. Then two years ago in Edinburgh, Rostropovich approached me and said he was taking over the National Symphony and said, 'I am asking all my friends for help.' So I agreed."

Rostropovich himself has been more blunt about how he persuades his "friends." His recruiting argument is straightforward: If they won't conduct for his orchestra -- he won't play his cello with theirs.

Abbado had only heard the National Symphony live on the radio, "and once, I believe, on television. Frankly, I was not all that impressed. Certainly I was not prepared for the quality of playing I have found here this week."

Abbado is one of a cluster of highly publicized young conductors who rose fast in the 1960s. He and the New York Philharmonic's Zubin Mehta studied together in Vienna. Both, in addition to Seiji Ozawa of the Boston Symphony, were assistants to Leonard Bernstein. All were regarded as glamorous wunderkinder .

Of the three, it was the career of Abbado that shot up the fastest. He became principal conductor in 1968 at Milan's La Scala, where he has been music director since 1971. Soon after that he also took on the Vienna Philharmonic, the oldest of orchestras, though he recently dropped that title to become principal conductor of the London Symphony Orchestra.

Abbado is indeed charismatic in looks. When not wearing his glasses he resembles a slightly stocky Dustin Hoffman, with dark complexion and longish black hair parted down the middle. He speaks splendid English, with a penchant for Americanisms like "sure," and "fine," and "okay."

"I guess that's because I learned the language in New York when I worked with Berstein," says Abbado.

He shows none of the flamboyance, or the temperament, that often goes with magnetism on the podium. "I get upset like everybody else, but I keep it inside of me," he says, gesturing resignedly to his chest.

He sat on a high stool before a rehearsal of the NSO Monday morning, clad in blue turtleneck and blue corduroys, with a blue ski jacket draped on the stool back (turtlenecks are standard, whether in rehearsal or when presiding over his baronial office at La Scala).

Unassumingly, he announced, "Let's begin with 'Beim Schlafengehn' ["Going to Sleep"] That's the third of Richard Strauss' 'Four Last Songs.'" This rehearsal was without the soprano soloist.

Abbado works with a subdued but intense concentration upon the work at hand, without ever seeming stern, much less autocratic. His interpretations are thought out in meticulous detail as to phrasing, timbre and dynamics. Thanks to his clear and simple conducting technique, he gets across what he wants quickly and easily. When there are problems he patiently works them out, one at a time. The end of the Mahler 4th Symphony's first movement begins with a quiet passage that must be very expressive, but on Monday the violins were a little too straight the first time around. So Abbado said simply:

"This must be broader, more rubato." And the next time around that was taken care of. Then he continued:

"Also softer. More pianissimo." Once through again and that was solved. Then he told the violinists:

"It must also have much vibrato." And on the third repetition it had "much vibrato."

Working out these three problems took about two minutes, without any confusion or friction. It might have taken much longer if Abbado, like many other conductors, had tried to deal with all three problems simultaneously.

When the five hours of morning and afternoon rehearsals were over, the orchestra gave him a tremendous ovation.

Later, a leading player observed, "I haven't seen anybody rehearse this smoothly since Stokowski. On Sunday night we started out ragged but he didn't bat an eyelash. He just worked away at it, without any tricks. The secret is that he knows exactly what he wants and he knows the best way to get it. And he's a real human. When he's in charge, everything comes out naturally in phrases and he reins in the sound enough that you don't have to force your instrument in order to be heard. But he made one thing clear pretty fast: You better give him pianissimo when he says so."

Despite the pressures of the havebaton, will-travel world, Abbado finds guest conducting relaxing.

"My wife, Gabriella, and my youngest son, Sebastian, who is 4, come along and I can spend more time with them than in Milan. Here, for instance, if there's a concert at night I can usually spend the day at home with them. There is also a girl who travels with us. She takes care of Sebastian and makes it possible for us to go out.

"But the truth is that we don't go out that much because Gabriella is a marvelous cook and I love to eat. And even I cook during our Julys in Sardinia." His specialties are Sicilian dishes. Abbado has two other children, Alexandra, 19, and David, 21, with whom he recently spent a skiing vacation in Switzerland.

He is going to have to cut back his touring. La Scala takes up a minimum of six months a year, and he's not about to give that up. "I can't imagine conducting opera regularly elsewhere than there. It's not only the remarkable orchestra and chorus, but, also, that the stagehands and the people who paint the scenery are very special."

Then there is London, where he conducts enough that the Abbados keep a permanent apartment there. So even Rostropovich may find it hard to get Abbado back to Washington soon.

"For the next two years, at least, I will be conducting in this country only in Chicago. There just isn't any more time," he says. CAPTION: Picture, Claudio Abbado, by Harry Naltchayan, -- The Washington Post