Police yesterday revealed they are investigating possible links between Austrian Josef Fritzl, who imprisoned and raped his daughter, and the unsolved murder of a young woman 22 years ago.

The bound body of Martina Posch was found on a shore of the Upper Austrian lake of Mondsee in November 1986. Fritzl's wife owned part of an inn and camping ground on the other side of the lake at that time.

"We have found no sign" of a concrete link up to now, a police spokesman said, but he added Fritzl would be asked for an alibi because he could have been in the area when 17-year-old Martina was killed.

The development emerged as doctors said the children at the centre of the Austrian dungeon ordeal and their mother were inching towards normal life in a spacious hospital wing.

Elisabeth Fritzl, 42, who has spent the past 24 years in a cramped cellar being repeatedly raped by her father, and two of her children who shared the tiny space with her, have the wing to themselves.

They are being treated along with another three of her children who were taken away at birth and raised by her 73-year-old father.

"The young people have space to play, they can run around," said Dr Berthold Kepplinger from the clinic near the town of Amstetten.

"The members of the family talk a lot, they are very happy to be together. They enjoy the food especially," he said, adding that yesterday the family had held an impromptu birthday party with a cake for the second-youngest child, 12-year-old Alexander.

The eldest child, Kerstin, 19, whose sudden illness led to the discovery of the scandal, was still seriously ill in another hospital on a ventilator.

Dr Keplinger said that, although all the others were relatively healthy, "there is a difference between those who had a normal life and those who lived up to 24 years in this dungeon". He added: "They have to get used to the daylight and space and room."

Authorities are trying to decide the future of Kerstin and her two brothers, Felix and Stefan, aged five and 18 respectively. Officials have discussed the possibility of providing new names for the children, who "never saw sunlight" until they were freed from the basement on Saturday.

Dr Kepplinger said Stefan could read and write in a "reduced form". He said Elisabeth had spoken "quite a lot" about what she went through in captivity, but he declined to provide details. "It was definitely dreadful for her and for her children," he said.

Meanwhile, Fritzl is refusing to talk to police or explain further why he put his daughter and her children through such an ordeal. His wife, who police still insist knew nothing of what was going on, has been allowed to visit Elisabeth and the children in hospital.

Since his initial confession on Monday, Fritzl has refused to talk to police. Franz Polzer, Lower Austria's top criminal investigator, said one detail Fritzl had divulged was that the heavy steel door shutting the basement dungeon off from the outside world was operated by remote control.

Fritzl faces up to 15 years in prison if convicted on rape charges, the most grave of his alleged offences. However, prosecutors said they were investigating whether he can be charged with "murder through failure to act" in connection with the death of a seventh child whose body was incinerated. That is punishable by up to 20 years in prison.

Authorities said that many question marks remained about Fritzl's life. His childhood is especially unclear. "I don't even know who his parents were," Mr Polzer said.

A Franz Fritzl is listed on a war memorial in the town of Amstetten, about 75 miles west of Vienna.

He apparently died in the Second World War between 1939 and 1945, but the city's government refused to say if it was Josef's father or not. Authorities said Fritzl has made a complete profile even more difficult by refusing to undergo more questioning.

Police also refused to comment on reports that Fritzl had a police record for other crimes - of which the files were erased under Austrian statutes of limitation.