Under the deal, Bankers Trust has agreed to exchange 0.83 shares of its stock for each share of Alex. Brown. That values the offer at $68.27 per Alex. Brown share.

The transaction's total value is almost $2 billion if Alex. Brown stock options are counted in the calculation.

The boards of both companies approved the deal over the weekend and the contract was signed.

"If you want to be a global player with the growth companies in the world and do a first-class job for your clients, you're going to have to have all of the products and services for the so-called one stop shopping," A.B. Krongard, chairman of Alex. Brown, said.

The new operation would be known as BT Alex. Brown.

The move could usher in more unions between banks and brokerage houses which traditionally have been prevented by a Depression-era law that bans banks from underwriting stocks. The U.S. Congress has been debating whether to repeal the law.

In February, Morgan Stanley merged with Dean Witter Discover, a brokerage and credit card firm.

Assuming the merger goes through, the combined firm would earn between 10 percent and 25 percent of its securities revenue from underwriting.

Alex. Brown is known for handling initial public stock offerings of small companies in the technology and health care industries. In the first quarter of 1997, it underwrote stock offerings worth $1.03 billion, sixth in the United States.

Brown had received many proposals but had turned them down. Bankers Trust, which has refashioned itself in recent years, was looking to transform itself into a full-service brokerage firm by getting experience in underwriting stocks, which Alex. Brown provides.

Stock of Alex. Brown (AB) jumped Friday on news of a possible merger, up 8-1/2 to 53-1/8 on the New York Stock Exchange. Bankers Trust (BT) fell 3/8 to 82-1/4. In Monday trading, shares of Bankers Trust fell 2-3/4 to 79-1/2, while Alex. Brown soared 9-5/8 to 62-3/4.