Alston W. Burleigh, 78, an actor and musician who taught in District of Columbia public schools for more than 21 years, died at his home in Washington Sunday of a circulatory disorder.

Mr. Burleigh was born in New York and came here as a youth. He graduated from Dunbar High School, served briefly in the Army during World War I, and then graduated from Howard University in 1922 with a bachelor's degree in music.

He began his teaching career as a substitute at Dunbar. He also taught in elementary schools. In 1927, he turned to the stage full-time and remained in the theater until 1940. In that time he toured the country with the Lafayette Players, worked with a stock company in Canada, and made some Broadway appearances.

In 1940, he went back to the Army. He was a major when he was released from active duty in 1944. He returned to teaching in Washington.

Mr. Burleigh taught in various public schools in the city. In 1958, he was assigned to Roosevelt High School, where he taught drama and music and started the Thespian Drama Group. He retired in 1969.

In the years after World War II, Mr. Burleigh took numerous courses in drama, speech and music at Catholic University and Columbia University in New York. He taught at Catholic University for one summer term.

Survivors include his wife, Erma J., of the home, a son, Dr. Harry T. Burleigh, of Clarksburg, W. Va., and three grandchildren.