Alexander Robertson Middleton, 77, a retired stockbroker and a former teacher and football coach at St. Albans school for Boys, died Tuesday at Sibley Memorial Hospital. He had emphysema.

Mr. Midlleton, who was born in Centreville, Md., attended Johns Hopkins University in Baltimore for two years and then transferred to Haverford College in Haverford, Pa., where he was captain of the football team and played fullback. He graduated in 1927.

He worked briefly for the IBM Corp. and then joined the faculty of St. Albans in Washington in 1928. He was a history teacher, athletic director and head football coach.

During World War II, Mr. Middleton was commissioned in the Naval Reserve and served aboard the aircraft carrier Bunker Hill in the Pacific. In 1944, he was transferred to the Navy's Iowa Pre-Flight Training School as head football coach. Among his assistants there was Frank Leahy, who became one of the great coaches in the history of Notre Dame University. He left the service with the rank of commander.

After the war, Mr. Middleton, who lived in Washington, joined the investment firm of Alex Brown & Sons as a stockbroker. He retired this June.

He was longtime member and former president of The Society of Colonial Wars.

Survivors include his wife, the former Frances DuBos Graman, to whom he was married for 46 years, of Washington; triplet daughters, DuBos Armbrister and deVismes Lee, both of Chevy Chase, and Mary Warner Schneider, of Oxford, Md.; one brother, Atherton, of Baltimore, and five grandchildren.

The family suggests that expressions of sympathy be in the form of contributions to St. Albans School for Boys, or to Christ Episcopal Church, Georgetown.