Citing "poor health," Ralph A. Beeton plans to step down on Dec. 31 as chairman and chief executive officer of First Virginia Banks Inc., a bank holding company based in Falls Church.

Beeton, who has guided First Virginia's growth since 1962, said Thomas K. Malone Jr., president of the firm, will assume the top positions.

Depending upon his health, Beeton will remain a member of the First Virginia board of directors and a consultant, the banking firm announced.

In relinquishing the title of chairman and chief executive, Beeton will be concluding active leadership of Virginia's oldest and sixth largest banking company, with 20 member banks, 163 statewide offices and assets of more than $1.3 billion.

When Beeton first was elected president of First Virginia in 1962, the company owned six banks with assets of some $185 million. He was elected chief executive in 1967 and has remained in that capacity since.

Malone joined the former Old Dominion Bank, a predecessor to First Virginia Bank, in 1950 and become its president in 1962. When Old Dominion consolidated to form First Virginia Bank, Malone was its initial president and chief operating officer. He was named the bank's chairman in 1974.

Two years later, Malone was granted a leave of absence to serve as chairman, trustee and president of the troubled First Virginia Mortgage and Real Estate Investment Trust - a REIT the bank company had sponsored. He returned to the holding company last February as president.

A native of Vermont, Malone is a graduate of the University of Vermont and of the advanced management course of the Graduate School of Business at the University of Virginia.

The 51-year-old Beeton previously served as chairman of the Association of Bank Holding Companies and president of the Virginia Bankers Association. He practiced law in Waynesboro and Arlington from 1954 to 1960, when he joined First Virginia as executive vice president.