The cases were among 14 the court added to its docket.

The court’s newest member, Justice Elena Kagan, disqualified herself from four of the new cases, including the one concerning corporate privacy, because she participated in them as United States solicitor general before joining the court in August. She has also recused herself from about half of the roughly 40 cases that had already been on the court’s docket for the new term, which starts Monday, and so will be absent from the bench much of the time in the coming months.

The state secrets case arises in a surprising context. The court has turned back appeals from people who say they were sent abroad to be tortured but whose lawsuits were dismissed after the government invoked the privilege.

This month, a sharply divided 11-member panel of the United States Court of Appeals for the Ninth Circuit, in San Francisco, dismissed a lawsuit against Jeppesen Dataplan, a Boeing subsidiary accused of arranging flights for the Central Intelligence Agency to transfer prisoners to other countries for imprisonment and interrogation, on state secrets grounds.

Boeing, as successor to the McDonnell Douglas Corporation, is one of the parties to the state secrets cases the court agreed to hear on Tuesday, Boeing Company v. United States, No. 09-1302, but now it objects to the government’s invocation of the privilege. Its case has been consolidated with the second one, General Dynamics Corp. v. United States, No. 09-1298.

Both arose from a 1988 contract to develop the A-12 Avenger aircraft. Dissatisfied with the contractors’ progress, the Navy terminated the contract three years later and demanded the return of $1.35 billion.