L. Muguel Borda, 36, a travel promotion officer in the U.S. Travel Service Office of the Department of Commerce died April 6 in Richmond, where he had gone on business.

A spokesman for the chief medical examiner in Richmond said the cause of death was a self-inflicted gunshot wound.

Mr. Borda was engaged in coordinating a Travel Service special market program in Venezuela and elsewhere in South America at the time of his death. He had joined the service in 1971 and had spent the next seven years stationed in Paris. He and his family lived in Annandale at the time of his death.

He was born in Stockholm, Sweden, where his parents were stationed in the Colombian diplomatic service. He lived in Spain, Japan and India, among other countries, before coming to the United States in 1960.

He had spent a year at the University of Delhi, India. When he arrived in the United States, he studied political science at Los Angeles Harbor College in Wilmington, Calif., and then went to the University of Mechigan, where he earned a certificate of proficiency in English. In 1970, he studied hotel management sales at Michigan State University.

Mr. Borda was a travel representative for the American Express Co. in Washington in 1964. A year later, he joined the State Department as an escort-interpreter. In 1967, he became senior sales representative for Air India in Washington. In 1969, he worked for a travel agency here and then rejoined the State Department as an escort-interpreter in 1970. He began his career with the U.S. Travel Service a year later.

Survivors include his wifr, the former Nellie Vecker, of the home; three children, Guy Miguel, Suzanne Alexandra and Jean-Paul, also of the home; his mother, Suzanne Broda, of Littleton, Mass.; a sister, Jacqueline Borda, of Washington, and a brother, Daniel, of Littleton. CAPTION: Picture, L. MIGUEL BORDA