A restless fraction of the American electorate did its best Tuesday to shake up the political establishment in eight states, and ended by paving the way for a "youth movement" into the Senate in November's elections.

On the heaviest voting day of the spring primary season, the voters beat incumbent senators in New Jersey and Montana and gave Senate nomination to six candidates who are 40 or under.

Conservatives did well in the nomination battles, as tax-conscious voters rejected emergency school levies in 15 Ohio cities and ordered a massive roll-back of property taxes in California.

The biggest conservative victory came in New Jersey, where 34-year-old Jeffrey Bell, a former aide to Ronald Reagon, ended the 24-year Senate career of Clifford P. Case, a 74-year-old leader of the GOP's small liberal wing.

Bell will face another 34-year-old newcomer, former basketball star Bill Bradley, who won impressively in a six-man Democratic primary field.

Conservatives also took satisfaction in the Iowa senatorial primary, where former lieutenant governor, Roger Jepsen, their favorite, defeated Maurice Ven Nostrand, the moderate candidate, for the Republican nomination against Democratic Sen. Dick Clark.

But in California, where a "tax revolt" wrote strong controls on property levies into the state constitution, Republican voters nonetheless gave the gubernatorial nomination to a veteran campaigner and middle-of-the-roader, Attorney General Evelle I. Younger, rejecting the bid of flamboyant conservative Ed Davis, a former Los Angeles police chief.

Younger will meet Gov. Edmund G. (Jerry) Brown (D), who won over nominal opposition.

Other familiar names who prevailed in Tuesday 'primaries included Ohio Gov. James A. Rhodes (R) and Iowa Gov. Robert D. Ray (R), early favourites for reelection.

The power of incumbency also showed itself in House races, as all representatives seeking renomination in the eight states came through unscathed.

The House also strengthened its reputation as a stepping stone to other offices as representatives gained Senate nominations in South Dakota, Mississippi and Montana, and Rep. Yvonne B. Burke (D-Calif., won a close race for the Democratic nomination for attorney general of California.

If elected, she would be the first woman and the first black to hold that post.

The Senate nominees who comprimse the potential youth movement include in addition to New Jersey rivals Bell and Bradley:

Rep. Larry Pressler (R.S.D.), 36, who became the favourite for the seat of retiring Sen. James Abourezk (D) after an impressive primary win.

Rep. Max Baucus (D-Mont.), 36, who defeated appointed Sen. Paul Hatfield (D) by a 3-to-1 ratio and put a strong claim on the Senate seat of the late Lee Metcalf (D-Mont.).

Rep. Thad Cochran (R-Miss.), 40, who won the first contested GOP primary in modern Mississippi history and now can sit back and wait while Democrats go through a runoff to select their contender for the seat of retiring Sen. James O. Eastland (D).

And New Mexico Attorney General Toney Anaya, 37, who was unopposed for the Democratic nomination agoinst Sen. Pete V. Domenici (R-N.M.).

Party leaders were generally cautious about interpreting the results of Tuesday's primaries, in part because the voter turnouts, except in California were extremely small.

But Democratic National Chairman John C. White noted that the "mood in the country is restless, and front-runners and incumbents aren ot safe."

Republican National Chairman Bill Brook put the same thought in stronger terms, saying the voting showed "the American people are just plained fed up. They are sick to death of government and taxes and they're looking for alternatives.

The Senate, at least, seems certain to be shaken up in the coming election.

A dozen members will not be back because of retirements or primary defeats. And for the first in many years, there will probably be more senators under 40 than there are over 70.

Here, in summary form, are the results in eight states that voted Tuesday.

In California, Attorney General Younger won the Republican gubernatorial nomination by a decisive margin. Younger had 40 percent of the vote in a four-way race, more than 7 percentage points ahead of former Los Angeles Police Chief Davis. Fresno assemblyman Kim Maddy and San Diego Mayor Pete Wilson trailed.

Among other things, Younger's victory demonstrated the power of television in California over a direct-mail campaign. Davis raised $2 million, twice the amount spent by Younger, but most of it was poured into a mail campaign run by Richard Viguerie of Fall Church., Va., the nation's leading direct-mail specialist for conservation causes.

Younger conserved his funds for a last-month television and radio campaign that featured low-key ads narrated by Art Linkletter, which stressed themes of competence and experience.

Brown defeated eight unknown opponents in the Democratic primary, receiving 77.4 percent of the vote.

The most recent Los Angeles Times poll gave Brown a 48-to-40 percent lead over Younger in a trial heat of the fall election.

In the race for the attorney general post being vacated by Younger, state Sen. George Deukmejian of Long Beach won the Republican nomination by a 2-1 ratio over James Browning Jr. of San Francisco, the prosecutor of Patricia Hearst. On the Democratic side, Burke won a 4 percentage-point victory over Los Angeles City Attorney Burt Pines.

In Mississippi, the identity of the Democratic nominee for the Senate against Cochran will not be known until a June 27 runoff. Maurice Dantin, who received strong support from allies of Eastland, edged out Gov. Charles (Cliff) Finch (D), who had been expected to lead the first round of voting in the seven-man Democratic field.

Dantin, 48, was viewed by Mississippi observers as the favourite to grab the majority from Finch, 51, in the runoff, with some party officials expressing fears that their battle may be divisive enough to add to the Democrat's problems in keeping Cochran from becoming the first Mississippi Republican senator since Reconstruction.

As a result of Tuesday's primaries, the lineup for other senatorial and gubernatorial races in the eight states is:

Iowa governor: Ray will go against Democrat Jerome Fitzgerald, the majority leader of the state House.

Montana Senator Baucus will be opposed by Larry Williams (R), 35, an investment counselor and political newcomer.

New Mexico governor: Former government Bruce King (D) will run against Joe Skeen (R), a sheep rancher who tried unsuccessfully for the office in 1974. Incumbent Jerry Apodaca (D) is ineligible to succeed himself.

Ohio governor: Rhodes' opponent in his bid for a fourth term will be Lt. Gov. Richard F. Celeste (D), 40. A major issue will be the state's school crisis, heightened by the rejection Tuesday of emergency tax levies in Cleveland, Columbus and 13 other cities, affecting 260,000 pupils. Many of the schools are now threatened by early fall closings.

South Dakota Senator: Pressler will be opposed by Donald Barnett (D), former mayer of Rapid City.

South Dakota Governor: Attorney General William Janklow (R) will face state Sen. Roger McKellips, who won the Democratic primary over Lt. Gov. Harvey Wollman. A tabulating error Tuesday night had Wollman the apparent winner over McKellips, who scored his upset with a personally financed television blitz. Wollman will serve as governor for five months this summer when Richard F. Kneip (D) retires to become ambassador to Singapore.