William F. Fallon Jr., 63, assistant circulation manager of the old Washington Daily News and then circulation director for another Scripps- Howard newspaper in Florida, died of cancer Monday in a hospital in Stuart, Fla.

Mr. Fallon joined the circulation department of the Daily News here in 1945 and remained with it until it was sold to the Washington Star in 1972 and ceased publication. He then became circulation director of the Stuart News in Stuart, a position he held until his death. He was associated with Scripps-Howard newspapers for more than 30 years.

Mr. Fallon had lived in Falls Church before moving to Florida. He was a member of the Arlington-Fairfax Lodge of the BPOE, the George Washington chapter of the Friendly Sons of St. Patrick, the Catholic War Vetrans, Post 1652, Falls Church, the national lodge of the Fraternal order of Police, and a lifetime honorary member of American Legion Post 130 in Falls Church. He also belonged to the Knights of Columbus and St. James Catholic Church.

His professional affiliations included membership in the International Circulation Managers Association and the Interstate Circulation Managers Association.

Mr. Fallon was born in Pittsburgh, Pa., and was a newspaper delivery boy while growing up there. He later was an advertising salesman for the Mckeesport, Pa., Daily News and the Valley Independent in Turtle Creek, Pa.

He moved to the Washington area in 1942 and worked for the Navy Department during World War II before joining the Daily News.

Survivors include his wife, Margaret of the home in Stuart: two sons, Michael T., also of the home, and Patrick C., of Falls Church; two daughters, Sharon Shreve, of Annandale, and Shelia Burgess, of Vienna; his mother, Margaret Fallon, of Vienna, and five grandchildren.