Nebraska voters yesterday gave Senator Robert F. Kennedy and former Vice President Richard M. Nixon impressive primary victories.

Kennedy, who scored just over 50 per cent of the vote in a three-cornered race, ran strong in almost every area and among every group in the conservative plains state.

Senator Eugene J. McCarthy said late last night that his 31 per cent showing was a "bit of a disappointment."

The big loser in yesterday's primary was Vice President Hubert H. Humphrey. Only 15 per cent of Nebraska's voters showed their support for him either by writing-in his name--which wasn't on the ballot--or by voting for President Johnson.

Humphrey was expected to get about 30 per cent of the vote in this conservative state. The Humphrey-Johnson vote was low even among blue collar workers and blacks who had been expected to give the Administration a substantial vote.

McCarthy ran far behind Kennedy in all areas except Lincoln, the home of the University of Nebraska.

Among Republicans, Nixon pulled nearly 70 per cent of the vote. California Governor Ronald Reagen won over 20 per cent of the Nebraska vote. The Governor did not campaign in the state, though his backers conducted a television campaign for him.

New York Governor Nelson A. Rockefeller got a six per cent write-in vote.

In a victory statement, Kennedy renewed his invitation to McCarthy to join in working together to change the course of the Democratic party.

But McCarthy said that he is going it alone into what he regards as the vital primaries in Oregon and California. The Minnesota senator said his showing will be better in Oregon and that California offers him his best chance of winning.

Kennedy's strength appeared to be coming from all sections of the state, in the rural areas as well as in the cities. In the 77 counties that reported returns, he was leading in 66. In three key Negro districts in Omaha, Kennedy ran up 282 votes to McCarthy's 12. The Vote 50 per cent tabulated Kennedy  38,486  53% McCarthy  22,442  31% Humphrey  7,102  10% Johnson  4,089  6% Nixon  56,575  69% Reagan  18,826  23% Rockefeller  4,348  5%