PARIS • It is one of the greatest and most popular art museums in the world and the only one in an old railway station.

Thirty years after the Musee d'Orsay opened its doors for the first time, it has become as much a Paris landmark as its big sister, the Louvre, just across the River Seine.

But the very success of the museum, best known for its unrivalled collection of Impressionist paintings is now causing it problems.

An average of 3.5 million visitors a year pour through its spectacular vaulted nave, making it the "most dense museum in the world", according to its director of collections, Mr Xavier Rey.

There is simply not enough space, he said.

Although the Musee d'Orsay is one of the top 10 most visited galleries in the world, it is several times smaller than its rivals.

"It will probably be difficult to welcome anymore visitors," said Mr Guy Cogeval, who heads the museum and its smaller offshoot the Orangerie, which houses Claude Monet's water lily murals.

Mr Cogeval, who is stepping down in March, said "one of the greatest challenges my successor faces is how to deal with this".

That lack of space was severely tested over the weekend when it opened its doors for free to celebrate its 30th birthday.

But the real problem is not so much the public as finding a place to show its staggering collection of late 19th-century and early-20th- century masterpieces, which runs from Courbet's notorious The Origin Of The World to Manet's reclining nude Olympia and Van Gogh's searing self-portraits.

While the museum is packed with some of Degas, Cezanne, Gauguin and Toulouse-Lautrec's best work, only about 4,400 pieces can be shown at any one time.

That leaves about 164,000 paintings and sculptures in its stores, which is set to grow even further with a Texan couple's donation of their €350-million (S$529.9-million) art collection to the French capital.

Businessman Spencer Hays and his wife Marlene last month approved the first instalment of 187 works for the Musee d'Orsay, including pieces by Degas and Modigliani worth about €173 million.

Their gift, the biggest from a foreign benefactor to France since World War II, also includes important work by Bonnard, Vuillard and Redon. About 140 works by Bonnard and Vuillard were also given to the museum in January by French collector Jean-Pierre Marcie- Riviere.

Faced with such pressure, the museum has bought a neighbouring 18th-century mansion on the banks of the Seine to house its library and research centre on the post-Impressionists.

The idea of a fine art museum in a railway station was revolutionary when the museum opened in December 1986. Not that the art deco terminus was your average transport hub.

Built like the Eiffel Tower and the Grand Palais for the Universal Exhibition in Paris in 1900, it had the same architectural exuberance.

Having survived demolition plans in the 1970s, it was converted into a museum for mostly French art dating from the revolutions of 1848 to the outbreak of World War I, one of the late French president Francois Mitterrand's "grands projets" to renew the French capital.

It was a runaway success from the start, equally praised for its architectural elegance and head-turning collection, such that "one can no longer imagine the museum anywhere but in this station", Mr Rey said.

Its biggest hit remains the exhibition questioning whether Dutch painter Vincent Van Gogh was really mad - Van Gogh-Artaud: The Man Suicided by Society - which brought in more than 654,000 people in 2014.

Another show featuring the artist will open in March.

Some of its biggest successes have surprised even its curators, as when almost half a million people flocked to see an exhibition this year on Rousseau, who was derided as a "Sunday painter" by his contemporaries.

A 2013 show on the male nude in art, Masculin, Masculin, which Mr Cogeval curated, was "to my great surprise a very big popular success with 430,000 visitors", he said.

The surprises do not end there.

The so-called academic painters from the mid-19th century who had long fallen out of fashion, such as William Bouguereau and Charles Gleyre, are now having an unexpected resurgence in popularity, Mr Rey said.

AGENCE FRANCE-PRESSE