Dominion Bankshares Corp. will begin offering discount brokerage services to its banking customers next week, becoming the first bank in Virginia to join the growing list of financial institutions offering services that once were the exclusive preserve of the securities industry.

A Dominion spokesman said the big Roanoke-based bank company will phase in the brokerage operations between Nov. 24 and Dec. 8, when Northern Virginia customers will be offered the service.

The actual buying and selling of stocks and bonds will be carried out by Bradford Broker Settlement Inc., a New York Stock Exchange member firm that already performs the same function for giant Crocker National Bank in California. Customer securities accounts will be held by Bradford.

But customers will deal directly with Dominion employes in the bank's new securities operation, Dominion Discount Brokerage Services. Orders will be transmitted by a computer link to Bradford's New York offices.

In the past few years, several hundred large and small banks have begun to offer similar brokerage services to their customers, and, earlier this month, several savings and loan associations -- including Perpetual American here -- set up brokerage offices in some of their branches.

The new S&L venture, called Invest, hopes to sign up several hundred thrift institutions by the end of next year.

Dominion will not set up brokerage offices in its branches, but instead will encourage customers to deal with its securities arm through an 800 telephone number. If a customer comes into a branch, bank employes will call Dominion Discount Brokerage in Roanoke, the Dominion spokesman said.

The spokesman said that Dominion's commissions will average between 40 and 70 percent less than those charged by full-service securities firms. Discount brokers buy and sell securities for customers, but do not provide many of the other services, such as research, that full-line brokers do.