ATLANTA — Pilots at Delta Air Lines Inc. and Northwest Airlines Corp. have approved a joint collective bargaining agreement. Ratification has been a key element of Delta's efforts to achieve a smooth integration of the two companies when it acquires Northwest later this year.

Delta's pilots union issued a memo detailing the results yesterday, the deadline for rank-and-file pilots of both airlines to vote. The agreement covers roughly 12,000 pilots of the two airlines.

Of eligible Delta pilots who cast a ballot, 61.74 percent voted in favor of the new agreement, while 86.76 percent of eligible Northwest pilots who cast a ballot voted in favor.

With ratification by both pilot groups, the joint agreement will become effective when the merger between Delta and Northwest closes, which is expected by the end of the year, Delta's pilots union said in a message to its pilots.

The pilots still do not have a deal to integrate their seniority lists, but have agreed to submit to binding arbitration if they cannot come to terms on their own by today. A three-member panel has already been chosen in case arbitration is needed.

Pilots value their seniority because it determines their schedule, the aircraft they fly and layoff protection.

Delta's stock-swap deal to acquire Northwest, announced April 14, is subject to shareholder and U.S. regulatory approval. European regulators cleared the deal last week.

The combination, being proposed at a time of persistently high fuel prices and airline industry financial woes, would create the world's largest carrier in terms of traffic.

The pilot agreement, together with a previous one reached between Delta pilots and management, calls for compounded raises for pilots over 18 percent over four years, a summary provided to Delta pilots says.

In exchange, the company will be able to place the Delta code and brand on Northwest flights and retain Northwest's large stake in Midwest Airlines, while maintaining those two carriers' separate operational status. The scope clause of the Delta pilot contract could have prevented Delta from doing those things had it not been amended.

The joint contract agreement also calls for pre-merger Northwest pilots to receive a 2.38 percent equity stake in the new Delta. Current Delta pilots would receive a 3.5 percent equity stake. The summary sent by Delta union officials to Delta pilots says the two amounts are proportional given the size of the two pilot groups. There are about 5,000 Northwest pilots and about 7,000 Delta pilots.