Southern Railway Co. and Norfolk & Western Railway Co. have terminated discussions begun in April aimed at a merger of the two railroads.

John P. Fishwick, president and chief executive officer of N&W, and L. Stanley Crane, chairman and chief executive officer of Southern, made the joint announcement yesterday. The simple statement said only that the talks aimed at consolidating the two companies under common corporate ownership and control were terminated without agreement. No further negotiations are planned, they said.

Spokesmen for the railroads declined to say why the talks had broken off.

A merger of the two, which would have required approval of the Interstate Commerce Commission, would have combined the nation's eighth and ninth largest railroads into a giant transportation line east of the Mississippi. Washington-based Southern has more than 10,000 miles of track in 13 southeastern states. The Roanoke-based N&W is the nation's largest coal-hauling railroad with 7,500 miles of track in 14 states and Canada.

N&W and Southern had contended their consolidation was necessary to maintain a competitive balance in the railroad industry if the proposed merger of the Chessis System Inc. and Seaboard Coast Line Industries Inc. went forward. That proposed merger is pending at the ICC. The proposed Chessie-Seaboard merger would create the largest rail line in the United States, linking the nation's fifth and seventh largest rails.