Norman C. Spencer, 68, a retired brigadier general in the Air Force who later worked for Resources Management Consultants in Washington, died of cardiac arrest Monday at the Malcolm A. Grow Medical Center at Andrews Air Force Base.

Gen. Spencer, who was born in Brookline, Mass., and grew up in Concord, Mass., graduated from the U.S. Military Academy at West Point in 1936. He later studied at the California Institute of Technology.

He became a pilot in the old Army Air Corps and a specialist in meteorology. During World War II, he served in Europe, and then became a command weather officer on the staff of Gen. Dwight D. Eisenhower at supreme allied headquarters.

After the war, Gen. Spencer joined the Air Force when it became a separate service, and held a number of staff and command posts in this country. sHe also graduated from the Industrial College of the Armed Forces, the Air Command Staff College and the Harvard Business School. Much of his later career concerned logistics. Among his assignments was that of chief of staff and director of operations of the Air Force Logistic Command for the southeastern United States. From 1963 until 1965, when he retired, he was director of materiel at Air Force headquarters in Washington.

Gen. Spencer then joined Resources Management Consultants, where he was technical director for overseas operations. He retired a second time in 1975. t

His military decorations include the Distinguished Service Medal, three Air Medals and two Legions of Merit.

Gen. Spencer, who had lived in McLean since 1965, is survived by his wife, Helen B. Spencer, of McLean; two sons, Allen, of Rochester, N.Y., and John of Ava, Mo.; two daughters, Sally Lowe of San Diego and Sandra Williams of West Lake Village, Calif., and seven grandchildren.