Germany's Stadelheim prison says doctors have determined that John Demjanjuk is fit enough to remain in custody.

Demjanjuk is being held on suspicion of acting as an accessory to the murder of 29,000 people at a Nazi death camp.

Had he been unwell, the 89-year-old retired autoworker could have been transferred to a hospital.

Anton Winkler, a spokesman for Munich prosecutors, said Demjanjuk "did fine" during his first night in prison and was doing well under the circumstances.

"There were no problems whatsoever," Winkler said. "He is still fit enough to remain in custody."

Munich prosecutors must still determine whether the former Ohio resident, who was flown to Germany aboard a private jet Tuesday, is fit enough to stand trial. But it could take up to two weeks for an expert to observe him and make a recommendation.

"We are nowhere near that," Winkler said.

Demjanjuk's lawyer Guenther Maull filed a challenge against his client's arrest warrant shortly after his arrival, arguing the evidence was not solid and Germany's jurisdiction questionable. The court is expected to rule on that in the coming days, Winkler said.

Demjanjuk says he was a Red Army soldier who spent World War II as a Nazi POW and never hurt anyone.

But Nazi-era documents obtained by U.S. justice authorities and shared with German prosecutors include a photo ID identifying Demjanjuk as a guard at the Sobibor death camp and saying he was trained at an SS facility for Nazi guards at Trawniki. Both sites were in Nazi-occupied Poland.

Efforts to prosecute Demjanjuk began in 1977 and have involved courts and government officials from at least five countries on three continents.