Cuthbert R. Train, 68, head of a Washington real estate firm that was founded in 1866, died in Hobe Sound, Fla., Saturday following a heart attack he suffered while playing tennis.

Mr. Train was a fifth-generation Washingtonian. He attened St. Alban's School and entered the real estate firm of Fitch, Fox and Brown after graduating from Princeton University in 1932. One of his grandfathers had been among the founders of the business.

Mr. Train was an avid tennis player. In 1962, he and his eldest son, Cuthbert R. Train Jr., won the District of Columbia father-and-son title.

Mr. Train was a member of the Metropolitan, Chevy Chase and Alibi clubs in the Washington area. He also was a member of the Quadrangle Club at Princeton and the Ausable Club near his summer home in Keene Valley, N.Y.

Survivors include four children by Mr. Train's marriage to the former Elizabeth Shouse, who died in 1967. In addition to Cuthbert R. Jr., of Greenwich, Conn., they are Mrs. Richard Longstreth of Manhattan, Kan., Jonathan A., of Louisville, Ky., and David, of Keene Valley, N.Y.

Also surviving are Mr. Train's second wife. Noel, of the home in Washington, and a stepdaughter, Mrs. Edward Terhune Miller, of Washington: two brothers, Middleton G. C. Train and Russell E. Train, both of Washington, and two grandchildren.

The family suggests that expressions of sympathy be in the form of contributions to the Children's Hospital or to St. Albans School in Washington.