That's ours. No, it's not. Who really owns culture?

In Greece yesterday Bill Clinton said Britain should return the Elgin Marbles, but he was told to stay out of the long-running saga

Just over a century ago, a British military expedition plundered the large 16th-century bronze doors of the royal palace in Benin city, Nigeria. Once they were in Britain, they were bought by the collector Frederick Horniman and placed in a museum named after him in Forest Hill, south London.

The doors - known as plaques - were not the only parts of the great Benin civilisation to have been seized by the West and, over the years, its people have made efforts to get them back. Yet this year's exhibition featuring the plaques at the Horniman Museum has received official Nigerian support. Why? Because the Benin people were consulted and Benin city museum's curator, Joseph Eboreime, acted as adviser. "It's been a huge success," Janet Vitmayer, the Horniman's director, said. "They felt we had done justice to their plaques. That justified, to some degree, the fact that we hold them here."

As the century draws to a close, the museum world is looking at who owns culture and what should be done with it. A trickle of claims for objects to be returned are landing on the desks of museum directors.

The row over damage done to the Elgin Marbles by cleaning at the British Museum 60 years ago has underscored these problems once more. They will be further aired when the findings of a six-member Greek team of conservationists are presented to a two-day international conference at the British Museum in 10 days' time. Although the Greeks look unlikely to reclaim the Marbles, taken from the Acropolis in Athens by Lord Elgin in 1801, each demand for restitution is assessed on its merits. And some of the biggest British museums are forbidden by their constitutions from disposing of objects in their collections other than under the most complicated conditions.

Earlier this year the Kelvingrove Art Gallery in Glasgow returned what was known as the Ghost Dance Shirt to the Lakota Sioux of North America who believed it had magical powers. It was worn at the Wounded Knee massacre.

But Dr Deborah Swallow, chief curator in the India and South-east Asia department of the Victoria and Albert Museum, London, believes objects should not necessarily be sent back. An exhibit, she explained, has a complex story, of which its origin is only one part. Many museums' most prized treasures have passed through numerous hands. "This is part of the history of the object and part of the history of these civilisations," she said. "The way we've approached it here is, first of all, to see ourselves as world custodians of these artefacts for everybody. We aren't the owners, we're the carers."

The artefacts of her own department, for instance, were the heritage of Britain's Asian community as well as part of the broader British heritage. Its duty was to inform those communities of this heritage. Thus, this year's Arts of the Sikh Kingdoms was developed in consultation with Sikh communities in Britain as well as India and the US. The issue of Nazi looted art, although distinct from rows such as those about the Elgin Marbles, has been the final spur to more determined action on claims for works to be returned. Many of Britain's leading museums have been searching their collections to check whether they hold any of the works which were seized from their Jewish owners during the Holocaust. The Tate's director, Sir Nicholas Serota, is chairing the joint working party.

A separate committee, under Dr Neil Chalmers of the Natural History Museum, was set up this year to investigate repatriation. Dr Chalmers said museums were great institutions because they had collections of objects and there would be concern if there were wholesale returns. But he said: "There is a steady flow of instances where museums are being faced with requests to return objects to communities. We think there's a lot of merit in establishing a good framework for handling these."

Andrew Graham-Dixon, the critic and presenter of the new television series on the Renaissance, said it was important to discuss each case on its merits. "In the case of the Marbles, you need to talk about what would have happened to them if they hadn't ended up here. The Marbles that have been left in place have been completely destroyed," he said.

He believed that, where possible, works benefited from being seen in context, such as the Bellini altarpiece which was designed for the San Zaccaria church in Venice and remains there.

"But I'm all for a bit of trade," Mr Graham-Dixon said. "We shouldn't give the Greeks the Elgin Marbles, but perhaps we should give them some Constables or Turners. Turner painted of the folly of human aspirations and how civilisations crumble. It would be a fruitful thing for them to ponder."