MANCHESTER, N.H., March 12--Former Vice-President Richard M. Nixon swamped all his opponents, as expected, in the New Hampshire Republican presidential primary today. He received about 81 per cent of the 92,000 GOP votes.

The write-in movement for Governor Nelson A. Rockefeller polled a poor 10 per cent of the votes. Rockefeller backers in the Granite State had hoped to garner 15 per cent of the primary votes.

In a press conference outside his New York apartment, Nixon declared that his overwhelming victory demonstrated "the general frustration of the country with President Johnson."

McCarthy Third

He attributed his victory to a "great organization" and his "effective personal campaign."

A Republican write-in for Senator Eugene J. McCarthy came in third behind Rockefeller with about 3 per cent of the GOP vote. Gov. George Romney, who withdrew from the 1968 presidential sweepstakes two weeks ago, lagged in a poor fourth with about 2 per cent.

Comparing his 80 per cent with President Johnson's 51 per cent of the Democratic vote, Nixon predicted tonight that a "new man would occupy the White House next January."

Key Victory

The Nixon victory is considered by most Republican Party observers to represent the key victory which the former Vice-President needed to dispel his loser image.

The 92,000 votes in the Republican primary were a bit heavier than expected, especially since a blinding snowstorm swept into the state during the late afternoon.