Two big names from Russia appeared at Avery Fisher Hall on Sunday afternoon: the violinist Vadim Repin and the pianist Nikolai Lugansky. They’ve been touring together, in places far-flung. Both musicians are in their mid-30s. Mr. Repin won just about every award and honor conceivable when he was a teenager. Mr. Lugansky has garnered his share of laurels, too.

And he has made several recordings that have set the world on its ear. The most recent one features Beethoven sonatas, and it contains playing of the highest order. I do not, of course, say “highest” lightly.

The Repin-Lugansky program on Sunday afternoon consisted of four excellent pieces, from Schubert to Part – though not in that order. The players dispensed with the chronological, which was wise.

They began with Bartok’s Rhapsody No. 1, a staple ever since the composer introduced it with his violinist friend, Joseph Szigeti. That was in October 1929 (a lousy month).

You can play the Rhapsody with a cool, modern sheen, which is how Joshua Bell played it in Carnegie Hall some weeks ago. Or you can play it earthily, rather “ethnically.” Mr. Repin chose the latter course.

He dug into the strings, like a hungry peasant. His intonation was imperfect, and he had other technical problems. But he was never out of control. When called on to provide a little lilt, he did so.

The pianist, Mr. Lugansky, played brightly and exactly. He is a disciplined, precise, brainy pianist. I have more than once written, when reviewing his CDs, “He’s the son of two scientists, and plays like it.”

Next on the program came the Schubert, which was his Fantasy in C, D. 934. Mr. Repin again had technical problems, including suspect intona tion. And there is often a fuzz on his sound, which he would do well to clean off.

But he had some very musical moments. (Hey, didn’t Schubert write some “Moments musicaux”?) For example, he sang the theme of the third section nicely. He knows that this is simple music, which you must not tamper with. But it was possible to play the ensuing variations with more charm and verve.

Mr. Lugansky’s Schubert was extraordinary. The pianist was almost shockingly clear and nimble – you never hear Schubert this way. And his passagework was so fluid, he might as well have been falling off a log.At some points, he created a kind of raindrop effect – making me think that he would be effective in Impressionism.

In a great many respects, Mr. Lugansky’s playing – crystalline, adept, refined – reminds me of Michelangeli’s. And what of that late master’s student, Martha Argerich? She can play like that, too, when her head’s screwed on right.

Both Mr. Repin and Mr. Lugansky should be given credit for unifying Schubert’s Fantasy. This is a sprawling work – it’s a fantasy! – and it can be unwieldy. These players made it seem logical, almost tight.

The second half of the program began with one of Arvo Part’s most popular pieces: “Fratres.” The violin version was written for Mr. Part’s fellow Balt Gidon Kremer. (Mr. Part is Estonian, and Mr. Kremer Latvian.)

Like many other works from this composer, “Fratres” should be played purely, cleanly, spiritually. It should certainly begin that way. Mr. Repin did not. He was all too rough and earthbound. Ideally, this music transports you; but on Sunday afternoon, we stayed firmly at Lincoln Center, New York City.

It’s true, however, that Mr. Repin built the piece decently, and whispered nicely at the end. As for Mr. Lugansky, he played his part with the purity, clarity, and awareness that “Fratres” demands.

The printed program ended with a beloved sonata, that of Cesar Franck. Mr. Repin rose to the occasion, playing nearly as well as his partner. The two had the measure of the first movement: It was neither blowzily Romantic nor wrongly reserved.

In the second movement (Allegro), Mr. Lugansky had some rare articulation problems, but he also demonstrated an A-1 fortissimo: thunderous but not banging. He and Mr. Repin filled the last pages of this movement with terrific excitement. When it was over, the audience applauded heartily, and it was perfectly right to.

The third movement was duly heartfelt, and the finale was winning. This music sometimes makes me think of a windmill, going round and round. Both players treated the melody splendidly, but they were very different from each other: Mr. Repin with his fat tone, Mr. Lugansky with his diamond-like one. The pianist missed some of his final notes, which was unfortunate. But then, a great many pianists do.

I should note here that violinist and pianist were at least equal partners in this sonata. When Brooks Smith (remember him?) played it with Heifetz – well, he accompanied him. (Heifetz wouldn’t have had it any other way!)

A final word about Mr. Lugansky: I had never heard him in the flesh, only on recordings. And, superb as those recordings are, you never know – the studio plays tricks. Would the guy be as good in person as on vinyl (or whatever they’re using these days)? The answer was yes, and what a relief.