The problem, David Usborne explains, is their Nazi past.
The Nazi-loot saga took an unexpected and emotionally charged twist yesterday following the news that authorities in New York are blocking the return to Austria of two paintings that had been on temporary loan to the Museum of Modern Art.
The move has delighted the two families who claim to be the rightful owners of the paintings by the Austrian expressionist Egon Schiele, Dead City and Portrait of Wally. Schiele died in 1918.
Both pictures were allegedly stolen by Nazi officers from family forebears before and during the Second World War.
"It's fabulous," said Rita Reif, an heir to Fritz Grunbaum, a comedian who died in Dachau in 1940 and owned Dead City.
"Now we can resolve what has been half a century of great loss."
But the confiscation is threatening to provoke a diplomatic feud between the US and Austria. It has, equally, caused dismay in the art world, stirring fears of long-term damage to the practice of inter-museum loaning.
The harshest reaction came from the Leopold Museum in Vienna, the current owner of the pictures. It had loaned the paintings to the Museum of Modern Art for a special travelling exhibition that ended last Sunday.
"There is no comparable instance in history," Klaus Schroder, the Leopold Museum's director, complained. "This could rise up to a very big scandal, and I'm afraid of that. I cannot say what will happen in the next hours or days."
The Leopold had already pledged to create a panel of experts to consider the claims of the two families and had promised to surrender the works if the ownership claims were upheld.
But Robert Morgenthau, the Manhattan District Attorney, served the Museum of Modern Art with a subpoena, forbidding the shipping of the pictures.
He is expected to insist they remain in New York while the case is considered by a special grand jury. The process could take months or even a full year.
Hoping to damp down the feud, the US embassy in Vienna yesterday said: "We believe the long-standing relationship of trust and co-operation between Austria and the United States will be helpful as the parties work to resolve this matter."