Two of the professors and the school's restaurant manager have died. When the disease was diagnosed in another music professor earlier this year public health officials moved to close the school, fearing it was contaminated by carcinogenic chemicals. The 1,500 pupils and 500 teachers moved out last month .
A scientific investigation, ordered by the Austrian Health Ministry, is being conducted in Vienna. Experts found high levels of polychlorinated biphenyls - better known as PCBs - in the school wallpaper, carpets and acoustic panelling. PCBs are toxic chemicals formed by burning or degrading plastics which are known to cause cancer in animals. High levels of phthalates, another constituent of plastic, were also found.
The source of the chemicals, which accumulate in fat in the body, remains a mystery. Experts suggest they may have been released into the atmosphere by a fire in a neighbouring building and then sucked into the school through its air-conditioning system. Another possibility is that they were released from some old electrical transformers nearby.
The building, which was opened in 1979, has an extensive air-conditioning system feeding its soundproofed studios and practice rooms. According to The Lancet, which carries a report of the school's closure, it was criticised from the outset because of its labyrinthine layout and windowless rooms and some politicians have called for the demolition of the building.
However, Austria's Ministry of Science and Education said the four cases were of two different types of leukaemia and stressed that the contamination had not been shown directly to be a cause of them.
British experts urged caution about the supposed link. Gareth Morgan, reader in haemotology at the University of Leeds and an expert on the causes of leukaemia, said: "These kind of clusters are very difficult to interpret. If they are different sorts of leukaemia in elderly professors they could have occurred by chance."
Dr Morgan said PCBs were known carcinogens but had no particular link with leukaemia. A one-off exposure even to a potent carcinogen would be unlikely to cause cancer but low level exposure over a long period could damage the DNA in cells and trigger malignant change.
He added: "We have never found much out about the clusters that have been investigated. But you can't disprove a link - there might be something going on."
The school was founded by Mozart's widow in 1841. Everyone who worked or studied in the building is being advised to get a medical check. A special counsellor is informing students and staff about the screening programme.
"Some people are so frightened, they don't want to go near the building," said Susanne Delinzee, a school spokeswoman.