NEW YORK, FEB. 2 -- A long-running power struggle at First Boston Corp., one of Wall Street's biggest and most prestigious investment banking houses, ended today with the resignations of four of the firm's top experts in mergers and acquisitions.

Takeover specialists Bruce Wasserstein and Joseph R. Perella, well-known deal makers who were responsible for much of First Boston's explosive growth during the past decade, led the group. They said they planned to start their own firm.

Wasserstein and Perella were among a handful of investment bankers who helped invent the modern corporate takeover game, and in doing so turned First Boston into a major player in that arena during the early 1980s. But their notoriety and power at the firm -- particularly that of Wasserstein -- rankled some at First Boston, including chief executive Peter T. Buchanan.

The resignations will hit First Boston's profits hard, analysts said, because the merger-related departments supervised by Wasserstein and Perella have reaped huge fees in recent years. First Boston's stock closed today at $24.37, down $1.87, or almost 8 percent.

First Boston named Richard H. Bott and James R. Maher, both managing directors of the firm, to replace Wasserstein and Perella. Bott and Maher declined comment. The firm today also reported a 1987 profit of $108.9 million, down from $180.6 million in 1986.

In addition to Wasserstein and Perella, two other top merger executives at First Boston -- managing director Bill Lambert and Charles G. Ward, one of the heads of the firm's merger group -- resigned. They said they will join the new firm, which will be called Wasserstein, Perella & Co. Inc.

The immediate cause of the resignations was a disagreement among First Boston's top executives over a recently disclosed restructuring and strategic plan for the firm. But Wall Street officials familiar with the firm characterized the resignations as the climax of a long struggle between Wasserstein and Buchanan over strategy and influence.

"We have a different vision of the future of the business than is reflected in the conclusions drawn from the recent strategic study," Wasserstein said in a statement.

As part of its restructuring, First Boston will lay off at least 550 employees, or about 10 percent of its work force. The layoffs already have begun.

Wasserstein and Buchanan disagreed over whether First Boston should commit itself to an aggressive strategy based on mergers and acquisitions, particularly in areas where the firm would use its own money to participate in takeover deals, Wall Street officials said.

There was a personal element to their struggle as well, the officials said. Young, aggressive and controversial, Wasserstein was profiled in magazines as a leader of the new generation of merger specialists who were changing the country's corporate landscape through takeovers. Often described as possessing one of the brightest minds on Wall Street, Wasserstein's personal reputation grew quickly as merger activity boomed.

Wasserstein said his new firm expects to have about 30 professionals initially and will provide merger advice as well as investments in takeover situations. The projected size of the firm would make it considerably larger than the so-called merger boutique firms that have sprouted on Wall Street in recent months.

Wall Street executives today disagreed about whether it was a propitious time to open a new mergers firm. Pessimists cited the slowdown in merger deals since the October market collapse as one inauspicious factor. But others said the personal reputations of Wasserstein and Perella would attract substantial business.

Like other big Wall Street firms, First Boston grew rapidly during the raging bull market of 1982 to 1987. Even before the market crisis, the firm had begun to study ways to rein in its expansion and establish controls over its stock and bond trading operations.

Last summer, the firm lost $100 million trading in options on Treasury bonds. The year before, it had a similarly large loss from trading in mortgage-backed securities. Wall Street officials said that Wasserstein favored integrating some bond-trading operations into an expanded merchant banking program, but that Buchanan, who used to be a trader, resisted curtailing the trading departments.

Wall Street officials said that the struggle between the two men finally became irreconcilable. Wasserstein considered leaving First Boston last year and discussed joining rival Lazard Freres & Co. After that spat with Buchanan cooled, Perella suggested the pair start their own firm if they ever left First Boston, Wall Street officials said.