George Deukmejian, a cautious, conservative Republican, succeeded unconventional Democrat Edmund G. (Jerry) Brown Jr. as governor of California today in perhaps the most dramatic of the gubernatorial turnovers produced in 11 states by November's elections.

The inauguration of Deukmejian, who promised tougher judges and criminal laws and a return to educational basics, contradicted the general trend.

While Republicans replaced Democrats this week in California and New Hampshire, Democrats have or will soon replace Republicans in Alaska, Arkansas, Michigan, Minnesota, Nebraska, Nevada, Ohio, Texas and Wisconsin.

However, Deukmejian was embroiled immediately in the sort of fiscal crisis threatening Democratic and Republican governors alike, and his approach mirrored the tendency of state officials across the country to move tentatively toward the difficult decision to raise taxes.

New Democratic governors have indicated that they might increase taxes on corporations or the wealthy, but most have realized that more general tax increases might be necessary to counter the effects of recession and federal budget cuts.

Michigan's first Democratic governor in 20 years, James J. Blanchard, has called for a state investment bank to help rescue a devastated state economy. Democrat Anthony S. Earl in Wisconsin has indicated that a 10 percent income tax surcharge might be necessary, and Democrat Richard F. Celeste in Ohio has spoken of increased taxes for high-income groups and corporations.

Deukmejian pointed out in his inaugural address here that the California state budget will have a $1.5 billion deficit by June 30. "We must make every effort to restore fiscal responsibility without a net tax increase," he said.

But most state leaders consider that impossible, and members of the Democratic-controlled California Legislature have become annoyed that Deukmejian has given them no help in finding a way out of their dilemma.

Instead, the former state attorney general focused on the law enforcement and pro-business themes that helped him win a narrow victory in November over Los Angeles Mayor Tom Bradley and provided such a strong contrast to Brown's outgoing administration.

California voters not only elected Deukmejian but also voted to build more prisons, approved a reform of the criminal justice system aimed at increasing convictions, and refused by a wide margin to freeze the number of privately owned handguns in the state.

In calling for what he termed "a Common Sense Society," Deukmejian said today, "It will be the highest priority during my administration to provide all the leadership I can to make California safe again."

Brown sat with other dignitaries on a platform outside the state capitol, wearing a coat with a fur collar to ward off the damp, 40-degree chill and seeming unperturbed by his 54-year-old successor's slighting references to his two terms in office.

Although defeated in his race for a U.S. Senate seat, Brown, 44, is expected to seek office again after a period of travel and what he calls "reflection." Perhaps more apparent than any other accomplishment of his eight years as governor, Brown left a state government and judicial system full of women, blacks, Latinos and other minorities who were not there before. In his last day in office he continued to fill posts, producing a glut of 25 judgeship appointments which included, for the first time, an avowed male homosexual judge in San Francisco.

To applause from a crowd of about 6,000 that was full of his supporters, Deukmejian said he wanted "a judiciary with a more balanced view" and would appoint "well-qualified men and women who will protect the rights of victims as well as protecting the rights of the accused."

Instead of Supreme Court Chief Justice Rose Bird, a Brown appointee and frequent target of attacks by Deukmejian, he had the oath of office administered by Justice Frank Richardson, the only high court judge appointed by a Republican governor.

Deukmejian began his administration with a ceremony full of band music, flags and honor guards that contrasted to Brown's more modest inaugural eight years ago. Brown had begun his governorship with a popular effort to promote an image of openness and frugality, but toward the end of his term he was perceived more as an eccentric.

Deukmejian said he planned to present the kind of image people expected of governors. In contrast to the makeshift inauguration night dinner Brown had at a favorite Chinese restaurant in Los Angeles, Deukmejian attended a $1,000-per-couple reception this evening and then went on to a gala inaugural ball that drew thousands.

Brown refused to live in a new $1.3 million governor's mansion, choosing a small apartment near the capitol building instead, but Deukmejian said he would like to move into the unused mansion. Brown is a bachelor who once dated rock star Linda Ronstadt, while Deukmejian speaks often and proudly of his wife of 25 years, Gloria.

The contrast between the two on the crime issue flared even before today's inaugural, when Deukmejian, as attorney general and member of a state commission on judicial appointments, vetoed three Brown appointees to a state appeals court.

One of the rejected appointees, San Francisco appeals court Judge Sidney Feinberg, waved his arms and shouted at Deukmejian, "What is it that you want, general? Are you going to have a litmus test for your candidates?"

"I'm not going to argue with you," Deukmejian replied. "I'm carrying out my responsibility as I see it."