ERBIL, Iraq  The semiautonomous region of Kurdistan is the one place in battered Iraq that promised economic boom times, but some of the foreign oil companies that rushed in over the past few years are becoming increasingly restless.

Their multibillion-dollar deals are still mired in a bitter political dispute between the Kurdish region and the central government in Baghdad.

They may have a stake in what is shaping up to be one of the greatest oil bonanzas of modern times, but the prospect of earning a profit, let alone recovering their costs, remains highly uncertain.

More potential headaches loom as public demands for scrutiny of local oil contracts for suspected improprieties have gathered momentum. The calls have come in the wake of revelations in November that a former American diplomat had a business relationship with a Norwegian company drilling for oil here, while also acting as a political adviser to the Kurds during the drafting of Iraq’s Constitution in 2005.