Democrat Michael Dukakis is off to a strong start in California and other longtime Republican strongholds in his race against Vice President George Bush, although a closely contested presidential election seems likely, according to an Associated Press survey.

The 50-state survey indicated widespread optimism among Democrats that Dukakis can end eight years of Republican rule in the White House. GOP officials in many states said the contest shapes up as a tight one, but several said Bush could win easily if he succeeds in his attempt to depict Dukakis as an heir to the Democratic Party's liberal past.Dukakis leads in the polls in California and New Jersey, which last voted Democratic in 1964, and is running even with Bush in the polls in Utah, which gave President Reagan his largest majorities in 1980 and 1984. One survey shows him running even in reliably Republican Nebraska, and within striking distance in Texas and Florida, key Southern states.

"I think it will be the closest presidential contest we've had since 1976," said Tom Cole, the GOP state chairman in Oklahoma. Oklahoma hasn't voted for a Democrat in a presidential campaign since 1964, but Cole said, "We don't have a candidate with Ronald Reagan's unique popularity. That's not to knock George Bush. Nobody else has got that kind of popularity either."

Said Democratic Chairwoman Karen Marchioro of Washington, "This is the best shot we've had in a long, long time." The last time a Democrat carried her state in a presidential election was 1968.

Republicans have won four of the last five presidential elections, with Jimmy Carter's victory in 1976 the only exception.

While Dukakis leads in nationwide public opinion polls, there is agreement that political fortunes in the five months until the election will be influenced by factors such as selection of a vice presidential running mate, campaign debates and the health of the economy.

Republicans believe that Dukakis' lead is a temporary result of favorable publicity over the past several weeks generated by his string of primary victories against Jesse Jackson.

"Nobody has laid a glove on Dukakis, and he hasn't been burdened with the traditional baggage a northern liberal carries with him," says South Carolina GOP party director Tom Denny. "That's going to change once the conventions are over. We haven't been able to start hitting on him."

For now, Dukakis' double-digit lead nationally is reflected in poll results around the country and optimism among Democratic officials in states from Washington and Oregon to New Hampshire.

- He leads Bush by a double-digit margin in polls in California. He is also viewed as the leader in both Washington, which last went Democratic in 1968, and Oregon, which last voted that way in 1964.

- Polls in Utah and Nebraska indicate the two men are running even. Neither state has backed a Democrat in a presidential race since 1964, and GOP officials in both states express confidence that won't change this time.