Although New York State considers the apartment to be rent-controlled, Mr. Kirschenbaum said he was not sure it qualified for that status, because it was the only residential unit in a commercial building. He added that the couple's lease, originally drafted 60 years ago, requires them to make repairs to the apartment.

Maddy Tarnofsky, the couple's lawyer, disagreed. "There is an ancient lease that does provide for the tenant to make certain repairs, but not structural repairs," she said, adding that she did not believe the provision would be enforceable in any event.

Ms. Tarnofsky contends that the rent sounds better than it is. "If you add in the amount they have spent over the years to keep the boiler running, and to do the types of repairs that are the responsibility of the landlord, it has actually been a very expensive apartment," she said.

The couple is now suing Mr. Kirschenbaum to force him to make further repairs to the apartment.

If the geopolitical situation were different, the prince and princess, who married in 1991, would have servants to handle such matters. Twelve years ago, Osman became the oldest male member of his family -- and thus the 45th head of the dynasty founded by Osman I in 1299. He is the last living grandson of any Ottoman emperor (his grandfather, Abdul Hamid II, ruled from 1876 to 1909). After him, Zeynep said, "the tradition of the family will disappear because the rest of the members were born abroad."

Their annual visits to Turkey are front-page news there. Turkey is seeking admission to the European Union, hat in hand, a process that some Turks find humiliating. By contrast, Osman symbolizes a time when the Ottomans exercised vast power.

He also represents a moderate approach to Islam. "If the caliphate were restored," Zeynep said, referring to the sultan's traditional role as the leader of Sunni Muslims, "the world would be a better place."

Born in 1912, Osman was sent to school in Vienna as a child. In 1924, the royal family was expelled by Kemal Ataturk, the founder of the Turkish Republic. "The men had one day to leave," he said. "The women were given a week."