DALLAS (AP) _ Southwest Airlines said Monday it agreed to buy ailing rival Muse Air Corp. for cash and stock valued at more than $60 million.

Southwest said Muse would continue operating as a separate airline under its current name, and would retain its current workers. Both Muse and Southwest are based at Dallas' Love Field.

Muse's chairman and founder, M. Lamar Muse, would become vice chairman of Southwest's new subsidiary, and the acquisition is subject to approval by Muse's shareholders and the U.S. Transportation Department, Southwest said.

Under the agreement, Southwest said each of Muse's 4.64 million common shares would be exchanged for $6 cash, 0.125 share of Southwest common stock and 0.125 of a five-year warrant to buy one Southwest share for $35.

Southwest's common stock closed Friday at $24.121/2 a share on the New York Stock Exchange. Muse closed at $8.621/2 a share on the American Stock Exchange.

All of Muse's 2 million preferred shares are owned by Almalgamated Sugar Co., which is controlled by Dallas investor Harold C. Simmons and which provided Muse with a $16 million infusion earlier this year.

Southwest said it would purchase each preferred share for $6 in cash plus accrued and unpaid dividends, 0.125 share of Southwest common stock and 0.25 of the warrant to buy one Southwest share.

Muse, which bans smoking on its flights, never recorded an annual operating profit since it was founded four years ago. In 1984, Muse lost $17 million on revenue of $101 million.

Muse primarily serves the southwest United States, and the profitable Southwest Airlines is its main competitor.

Muse Air was founded by Lamar Muse and his son Michael after the elder Muse left Southwest in 1978, where he had been president and chief executive since 1971, when that carrier was founded.

Lamar Muse retired from Muse Air last May. Muse Air than ran into severe financial trouble before it was able to secure the financing from Simmons. However, the investment was conditioned on Lamar Muse's return as Muse Air's chairman and chief executive, succeeding his son.

While some scheduling changes may be made to take advantage of the medium- and long-range jets in Muse's fleet, Muse will continue offering the same type of service it offers now, Southwest said.

Southwest Chairman Herbert D. Kelleher, in a letter to his employees, said the merger would help both airlines and he asked for cooperation.

''This proposed acquisition is in the best interests of the shareholders and employees of both carriers, and I hope that each of you will express to the Muse Air employees your delight that we are going to be working together rather than against each other in the future,'' Kelleher said.

Southwest serves 24 cities in 10 states - California, Arizona, Colorado, New Mexico, Louisiana, Missouri, Illinois, Arkansas, Nevada and Texas. Southwest earned $49.7 million in 1984 on revenue of $535.9 million.

Muse serves 10 cities from Dallas - San Jose and Los Angeles in California; Las Vegas, Nev.; Tulsa, Okla.; New Orleans; and Houston, Austin, Brownsville, Midland-Odessa and McAllen in Texas.