In separate actions yesterday, stockholders of both Southern Railway Co. and Norfolk and Western Railway Co. approved in overwhelming fashion the proposed merger of the two companies.

Meeting in Roanoke, 99.2 percent of N&W's stockholders who voted favored the proposed consolidation, while Southern's stockholders approved the proposed merger in Richmond with 99.3 percent of the ballots cast favoring the combination.

The merger proposal would create an 18,100-mile eastern rail system stretching from Montreal, Buffalo and Detroit down to New Orleans and Florida, and from the East Coast to Chicago, Omaha, Kansas City, St. Louis and Memphis.

The agreement approved yesterday would bring the two companies under common ownership and control by the formation of a new holding company called NWS Enterprises.

The boards of directors of both companies had approved the plan earlier and had recommended its approval by the stockholders. Terms of the agreement call for N&W stockholders to receive one share of stock in the new holding company for each share of N&W common stock. Southern stockholders are to receive 1.9 shares of stock in the new company for each share of Southern common.

The next step in the merger process for the two successful rails is formal application to the Interstate Commerce Commission, which then has 31 months to make a decision, although it has been trying to act more quickly when it can. N&W Chairman John Fishwick said yesterday the application would be filed Dec. 1.

Officials of Southern and N&W held merger talks last year over a seven-month period and abandoned them without an agreement. But this year, citing the "changed competitive situation" in the railroad industry, they got together again and worked out the new merger plan. The merger trend in the industry and the changed deregulation climate were important factors, they said, noting that a combined Southern-N&W would be able to compete more effectively with the merged Chessie System and Seaboard Coast Lines, a combination that became effective last week.

At yesterday's meetings, 81.7 percent of the total outstanding shares of N&W common stock entitled to vote were cast and 79.5 percent of the total outstanding shares of Southern common and preferred entitled to vote were cast.