NEW! NEW! NEW! NEW!

When the Bolsheviks enlisted the avant-garde in their revolutionary struggle Russian art was transformed.

We are revealing new pages of art in anarchy's new dawns. We are the first to come to the new limit of creation. Like a new planet on the blue dome of the sunken sun, we are the limit of an absolutely new world."

New, new, new, new, new! These announcements, and others like them, appear on the caption boards of New Art for a New Era, an exhibition of Russian revolutionary art at the Barbican Gallery. The announcer here is the show's presiding figure: artist and tub-thumper, Kazimir Malevich. He was the limit. If artists talked themselves up like this nowadays, we'd think they were mad or joking.

Was Malevich? You may wonder whether any art - even art of a devastating originality, for example Malevich's own 1915 painting, Red Square - could warrant such clamour. And perhaps this manifesto-language can be written off as sheer exaltation and hyperbole: period art-speak. Fun at the time, even needful, but really irrelevant to the work it helped launch. Or are we missing something?

In the gallery, that's pretty much how the slogans work. They up the tempo, advertise, add atmosphere and an air of excitement. And any show in Barbican's upper gallery needs all the airs it can get. This is an odd collision: one the most dynamic episodes of modern art, displayed in one the most deadening exhibition spaces in the world. And the Barbican wins; it always does.

But you can see the pictures are putting up a spirited fight. They're all on loan from the State Russian Museum. But they all originally belonged to the St Petersburg Museum of Artistic Culture. This was one of numerous cultural institutions and initiatives set up in the immediate wake of the Bolshevik revolution. It was established in 1919 as an artist-run public collection, with Malevich and Tatlin among those in charge, displaying all the succeeding avant-gardes of Russian art since the start of the century. The pace is hectic: Post-Impressionism, Cubism, Futurism, Cubo- Futurism, Rayonism, Suprematism, Constructivism were all represented in the Museum.

But the enterprise was also political, in the most literal way. It was one more sign of the "leftist dictatorship of the arts", the victory of contemporary avant-garde artists, over artistic conservatives, for the favour of the revolutionary government. The Museum of Artistic Culture was their place in history - except that neither the favour, nor the Museum, lasted much beyond the mid-Twenties.

People have been known to get very wistful about this brief but fervent episode. The relationship of Bolshevism and avant-gardism: it's a radicals' Camelot, the only real example of a revolutionary politics in alliance with a revolutionary art, and so soon cut short. It's startling that any government, with a lot of grass-roots work to do, should look to post- Cubist art for a helping hand in geeing up the populace. Of course, this confidence didn't last. Stalin sponsored a cultural turn-around under the name of Socialist Realism, and the art-conservatives were back in business.

Then again, it's not obvious that advanced art should be politically progressive. But the Russian avant-garde was actually quite prepared for the revolution - or some sort of revolution. They could hardly avoid the issue. If you think your society is on the verge of total disintegration, which had been all too thinkable in Russia for some time, and if in the studio you're turning out absolutely unprecedented visions of chaos, energy and strange new orders, you only needed to be a little bit of a megalomaniac to start making connections and thinking about the shape of things to come.

This exhibition is good at showing how staggering these visions must have been - simply because some of them haven't been seen much in the West before, and their strangeness really is still new to us; Pavel Filonov's work, for instance. Two pictures here, Flowers of Universal Blooming and The German War, both 1915, are derivatives of Cubism, but they make Cubism look bizarre again, by breaking its normal habits: using lurid colours, fragmenting the image into tiny slivers, packing them claustrophobically tight, and then doing it all on a very large scale. The effect is horrible, I think, but you have to admit you've never seen anything like it. The catalogue says, without elaborating: "Filonov's idea of a universal flowering led him to seek in his painting a way of showing the concept of a lost harmony in human existence." It doesn't sound very Leninist. But after the Revolution, he was doing ideology work for the Museum.

The art points in wildly divergent directions. Sometimes its back to the folk. Mikhail Larionov's Venus (1912), is a folky-primitivist image, with a bright yellow woman in a bold wonky outline, and the title, date and artist's first name written in big letters on the picture. Larionov was into icons, sign-painting and popular prints. The subject is "classical", but he's trying to come across as a kind of peasant-artist.

And sometimes it's "Forward with Industry". Take this manifesto from the following year. "We declare the genius of our days to be: trousers, jackets, shoes, tramways, buses, aeroplanes, railways, magnificent ships - what enchantment - what a great epoch unrivalled in world history. We deny that individuality has any value in a work of art." That was Larionov, too, now being a techno-crazy Rayonist. And that "down" on individual creativity certainly came on in force after the Revolution. Chagall got heavily criticised for it.

Or it can be hard to say precisely what's being envisaged. Malevich himself, when he's talking, is almost impossible to understand: a voice of apocalyptic, euphoric nihilism, affirming some enormous transformation founded on "nothingness". The actual Revolution could, at least at first, be felt to embody a variety of imagined new eras, and welcomed as such. And it sometimes seems that Malevich thought political events were very much secondary to some greater dawn he had in view.

The odd thing about his pictures is that though they're an extremely radical reduction of pictorial means - pure colours and plain shapes on a white ground - and sometimes with a good deal of hit, they also have a very gemutlich feeling in their sturdy but snug paintwork, in the slighty wobbly lines of their geometry, and in the way you can almost make up "Hello, Mr Triangle" stories about the bits and pieces.

But clearly this isn't at all what Malevich felt. Perhaps other agendas have become invisible. David Shterenberg's Still Lifes from around 1920 are among the show's most beautiful new items (new to me): very few elements, painted pretty flat and flat-on, viewed on the table-top from overhead, and painted almost without a personal style. The painting rather finds a style in response to each object depicted, sometimes imitating its texture overtly, and this makes a nice, staccato discontinuity among the parts. And was this way of doing it a deliberate avoidance of individuality? Did it somehow also feel politically correct?

But one painting here makes its cause very plain, though the cause is hardly more specific than "possibility" - which is just what made it such a potent icon of revolution. This is Vladimir Tatlin's marvellous Sailor, 1911, maybe a youthful self-portrait, certainly a kind of portrait, but a portrait where everything is on the hop, provisional. You have the head turned, looking out to one side - the shapes of cap and uniform whisked together - the face formed from swipes of ochre and white, which work as rather arbitrary modelling, but could equally be painting that's been left off, half-done - and then a surprising touch with the eyes, mere dabs of deep blue with a black dot, as cheap and nothing-up-sleeve a trick as the rest in this image, but (when you might have expected a blank puppet) giving a sudden access of life and soul. An identity improvised from the brief coincidence of its parts. A new man, at every moment.

New Art for a New Era: Barbican Gallery, Barbican Centre, Silk St, London EC2; everyday till 27 June; pounds 6, concs pounds 4 (admits also to David Bailey: Birth of the Cool)