NationsBank Corp. and BankAmerica Corp. said today they are merging to create a coast-to-coast banking giant, and Banc One Corp. is combining with First Chicago NBD Corp. to create the dominant bank in the Midwest.

The two mega-mergers come after last week's planned union of banking giant Citicorp and brokerage and insurer Travelers Group raised the stakes for other financial companies that already were consolidating to compete.

NationsBank, based in Charlotte, N.C., covers the Southeast to Maryland. BankAmerica spreads east from its San Francisco base. Together they would have $570 billion in assets, making it the nation's biggest bank ahead of Chase Manhattan Corp.

The combined bank, which will take the BankAmerica name, will operate in 22 states.

``We've built a truly national franchise with this ideal partnership,'' said BankAmerica chairman and chief executive David Coulter, who will become president of the combined bank.

The Banc One-First Chicago combination, to be known as Banc One, will create the fifth-largest banking company in terms of assets, at $230 billion.