Joseph I. Nachman, 73, who worked for the National Labor Relations Board for nearly 35 years before retiring as an administrative law judge in the mid-1970s, died Friday at Alexandria Hospital. He had leukemia.

He joined the NLRB in 1942. He was a supervisory trial lawyer and deputy assistant general counsel before becoming an administrative law judge in 1962. After retiring, he maintained senior judge status until his death.

Mr. Nachman was a native of Balitmore. He was a graduate of the University of Virginia and earned a law degree at the University of Maryland. Before coming to Washington he had maintained a private legal practice in Staunton, Va.

He was a member of the American, District of Columbia, Maryland, and Virginia bar associations.

Mr. Nachman, who lived in Alexandria, was a member of the Beth El Hebrew Congregation of Northern virginia in Alexandria and also belonged to B'nai B'rith.

His first wife, the former Rose Polansky, died in 1964.

Mr. Nachman's survivors include his wife, the former Eva Cohen Kopp, of Alexandria; a son, Alvin, and a daughter, Lois Buckman, both of Baltimore; a stepson, Philip Kopp of Virginia Beach; a stepdaughter, Eunice Cook of Long Island; three brothers, Leon, of Falls Church, Dr. Herman, of Richmond, and P.M. Nachman of Alexandria; a sister, Rose Ella Kanter of baltimore, and eight grandchildren.