Robert G. Tillotson, 58, an executive director of the National Museum of American History of the Smithsonian Institution, formerly the Museum of History and Technology, died of a brain tumor May 18 at Fairfax Hospital. He lived in McLean.

Mr. Tillotson moved to Washington in the mid-1960s and joined History and Technology in 1966. He held various administrative posts, being named executive director of the national philatelic collections in 1979.

He was a specialist on museum security and was a former chairman of the International Committee on Museum Security of the International Council of Museums. He published a book, "Museum Security," in 1977.

Mr. Tillotson was a native of Hiram, Ohio. He served in the Army Air Forces in Europe during World War II. He was a graduate of Franklin College of Indiana and attended Indiana University's graduate business school. He was associated with museums in California, Massachusetts and Ohio.

He was a volunteer with the Central Fairfax Services for Retarded Persons.

Survivors include his wife, Joan U., of McLean; three daughters, Ann Tillotson of McLean, and Prudence Tillotson and Jane T. Buker of Santa Barbara, Calif.; a son, John R., of New York City, and a sister, Jean LaFollette of Munster, Ind.