Hitler, Stalin and Mussolini used art to cement their power, reports. An immense building project is underway in Moscow to recreate Russia's largest church. The Cathedral of Christ the Saviour, 30 storeys high, dominated Moscow's skyline until Stalin ordered its demolition in 1931.

Dictators well understand the value of grand structures in the public drama of power. This edifice symbolised an authority communism was dedicated to eradicating. In its place Stalin planned the biggest building in the world - The Palace of the Soviets, topped by a huge heroic figure of Lenin.

The outbreak of war scuppered the plan and the would-be palace's foundations later became a swimming pool. Now the Orthodox Church is rebuilding the cathedral amid controversy over rising Russian nationalism.

Across Europe, in Berlin, another project is beginning. The Reichstag, home to Germany's parliament from Bismarck to Hitler, is to be restored by British architect Norman Foster. He describes his plans as the "realisation of a philosophy about openness and accountability" - a vision rather different to that devised for Berlin by Adolf Hitler. He envisaged an array of symbolic architecture that would glorify the Reich. Albert Speer's designs for Hitler, which included grand avenues, a triumphal arch and a massive assembly hall, were not realised, but Europe is littered with architecture offering reminders of the cultural landscape of this century's great tyrannies and the way they co-opted art in their cause.

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Such relationships lie at the heart of the exhibition Art and Power: Europe under the Dictators, which opened yesterday for a three-month run at the Hayward Gallery, London, and which concentrates on Hitler, Stalin and Mussolini.

In an essay introducing the exhibition, the historian Eric Hobsbawm defines three demands which power makes of art: to demonstrate its triumph, to propagandise on its behalf and to organise power into public drama.

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Hobsbawm writes: "Ritual and ceremony are essential to the political process and, with the democratisation of politics, power increasingly became public theatre with the people as audience and. . . this was the specific invention of the era of dictators . . .(with the people) as organised participants."

The cold war era tended to emphasise the cultural affinities between fascism and communism. This show highlights similarities while also allowing us to explore fundamental differences; crucially, in their claims to authority and how this informed their approach to culture. Both Hitler and Stalin ruthlessly limited free expression and saw art as having duties rather than privileges. David Elliott, director of the Oxford Museum of Modern Art and one of the show's curators, says: "The aesthetic foundation upon which all modern art has been built . . . the notion that an artist's individual conscience or sensibility can lead to personal or universal redemption . . . was clearly intolerable to the dictators.

"When faced by the naked reality of power, art's fragile autonomy soon crumbled. In the brave new world of dictators, the idea of an avant garde could seem either like an unwelcome reminder of the past or a rallying point for counter revolution. It was, accordingly, one of the first manifestations of the older order which had to be obliterated."

In Russia the vibrant avant garde experiments of the 1920s by artists like Malevich and Taitlin soon succumbed to the demands of the state. The Nazis were even quicker to eliminate art that did not serve their purposes.

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Nazism's need for an art glorifying a mythologised past to legitimise the present was poorly served by plastic artists. Sculptors like Arno Breker and Josef Thorak, painters such as Fritz Erler and Oscar Schlemmer failed to deliver and disappointed the Fuhrer, who eventually expressed the hope that "some artists of real stature" would emerge to glorify his achievements.

Film maker and writer Lutz Becker, another of this show's curators, says: "National Socialism never acquired the strength to stimulate original artistic personalities. It only activated artists who would have been otherwise marginalised by the progress of modern art."

Nazism fared better in creating public spectacle to match its vision - something that the Soviets rarely achieved. Hitler was well served by Speer's mass rallies - rituals to match Hitler's oratorical power - including the Nuremberg rally, recorded by one of the Reich's other rare talents - film maker Leni Riefenstahl, whose two films, Triumph of the Will and Olympia remain among Nazism's most powerful documents.

The exhibition stops in 1945. New lines of force were emerging and the locus of political power and artistic creativity had been shifted westwards by Europe's tumult.

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But the fate of art subservient to the state holds lessons for today. Elliott notes: "For a free society, art is both a reflection of its complexity and an intimation of its capacity for change. As a result modern art - almost by definition - often has an incompatible or critical relationship with the culture in which it is made . . . Like a canary down a coal mine, its state, no longer allied to power, but dependent upon it, may be an indicator of potential disaster."