The Russian National Orchestra played in Avery Fisher Hall on Tuesday night, and they will play again on Sunday afternoon. The RNO is playing nothing but Russian music on this visit. There is no reason a Russian orchestra should have to play only Russian music, any more than the New York Philharmonic should have to stick to Ives. Besides which, Tchaikovsky, Rachmaninoff, and the like are universal composers.

At any rate, the RNO was conducted on Tuesday night by Vladimir Jurowski. He is in his mid-30s, and has masses of hair — conductor’s hair. He looks like Hollywood’s idea of a conductor. On Sunday afternoon, the orchestra will be conducted by its founder, Mikhail Pletnev. He doubles in life as one of the world’s best pianists.

The program on Tuesday night began with Stravinsky’s “Scherzo Fantastique,” Op. 3 — an early work, as you can tell from its opus number. Stravinsky wrote it when he was about 25, and it is a delightful thing: light, sparkling, Mendelssohnian. (Think “A Midsummer Night’s Dream,” Russified.) Rarely is a piece so perfectly named — “Scherzo Fantastique.”

Under Mr. Jurowski, the RNO was competent, hanging together in a work not easy to execute. But there should have been more intensity in the performance, less relaxedness. You should have been closer to the edge of your seat. The viola contributed a fine solo, and the flute did well, too.

Then came a big concerto, Tchaikovsky’s Violin Concerto, played by Leonidas Kavakos, the young Greek. He also works as a conductor, leading the Camerata Salzburg. And he is a thoughtful, skillful, talented musician, in either of his roles. Last November, he played the Berg Concerto with Christoph Eschenbach and the Philadelphia Orchestra in Carnegie Hall. That was one of the best concerto performances we have had this season.

And how about Tuesday night? Well, you know how you can sometimes tell a performance will be good in the opening measures? This was one of those occasions. From the outset, Mr. Kavakos was assured, smart, and compelling.

He went through the first movement with heart and fire, but no bombast. He was individualistic but not eccentric. He made a beautiful sound — virile, thick, and, frankly, loud. That sound at times blew your ears back, which is not supposed to happen in Avery Fisher Hall from so small an instrument.

The theme of the second movement, Mr. Kavakos stated simply and intelligently — no baloney, all musicality. And he took the last movement very fast, playing it brilliantly. He did wonderful things with rhythm, enhancing the music rather than distorting it. He also showed off, just a little, as is appropriate in a vehicle like this: He took his left hand off the violin, working with just chin and bow.

There were problems in this account — mainly bad intonation toward the end of the first movement. But you would not want to complain about a performance like this. The Tchaikovsky concerto has life in it, and forever will, as long as there are people to play it justly.

After the first movement, the audience applauded at length — they wouldn’t stop. Mr. Kavakos finally acknowledged this applause with a sheepish, perhaps slightly annoyed, nod of the head. There was no need to be sheepish or annoyed, and he should have bowed, rather than nodded. At the end of the concerto, the audience applauded and applauded — and applauded and applauded. After many curtain calls, Mr. Kavakos gave them “Obsession,” a movement from an unaccompanied sonata by Ysaÿe.

The word “diabolical” is overused in discussion of violin playing (Paganini, Tartini, and all that). This playing was truly diabolical.

Mr. Jurowski and the Russian National Orchestra closed the program with Prokofiev’s Symphony No. 5, which they played capably. At its best, this performance was full of character, “authentic” seeming. The music growled and staggered, sang and marched. Sound was nicely and rightly unpolished (but not ugly). At its worst, the performance was unremarkable. The second movement — Allegro marcato — can be much more wondrous, wacky, and exciting than the RNO showed.

Yet, at the finish, the audience applauded endlessly — endlessly. Most performers will play an encore at the drop of a hat, whether they’re asked to or not. Mr. Jurowski had to be practically begged. Finally — with maybe a quarter of the audience remaining — the orchestra played the waltz from Prokofiev’s “War and Peace.” This was haunting, though the concluding pizzicatos were terrible. Possibly the worst in the history of music.