WASHINGTON (AP) _ Voters may get the idea they're watching reruns in some states this fall.

Gubernatorial rematches, with the sitting governor facing a familiar foe, are under way in California, Arkansas, Illinois, Ohio and Texas.

And in at least four more states, former governors are trying to regain that old glory after a hiatus of as many as 20 years.

''It's not so much they want to dust off the epaulets,'' said Michelle Davis, executive director of the Republican Governors Association, explaining the attraction for former governors to run again. ''It's that it was the best job they ever had.''

The rematches include some of the biggest states and most hotly contested of the 36 governors' races in 1986:

- Texas. Former Republican Gov. Bill Clements leads the polls against the Democrat who unseated him four years ago, Gov. Mark White, who is beset with a disastrous economy and criticism of his school reforms. Clements, the only GOP governor Texas has elected since Reconstruction, hoped to get a boost as well as some money from President Reagan's visit last week.

- California. Republican Gov. George Deukmejian is leading in his bid for a second term against Los Angeles Mayor Tom Bradley, a Democrat who lost by less than 1 percentage point to Deukmejian in 1982. Bradley is trying to become the nation's first black governor.

- Ohio. Republican James Rhodes, governor for 16 years, is trying for a fifth term against incumbent Democrat Richard Celeste. Celeste barely lost to Rhodes in 1978, then won four years later. And another face from the past, Cleveland's former maverick mayor Dennis Kucinich, is running as an independent.

- Arkansas. Democratic Gov. Bill Clinton knows his opponent well. Republican Frank White unseated Clinton in 1980, then lost to Clinton two years later. Clinton easily defeated another Republican in 1984. This year, Arkansas switches from two-year to four-year terms.

- Illinois. What was to be a rematch between former Sen. Adlai Stevenson and GOP Gov. James R. Thompson, who narrowly defeated Stevenson in 1982, has become a legal battle over Stevenson's bid to get on the ballot as a third- party candidate. He renounced the Democratic nomination won in the March primary because his running mate, the lieutenant governor nominee, is a disciple of extremist Lyndon LaRouche.

In Tennessee, a former GOP governor from the early 1970s, Winfield Dunn, is trying to win his old job, as is Oklahoma's former GOP Gov. Henry Bellmon, who later served in the Senate after leaving the governor's office in 1967.

Idaho's former Democratic Gov. Cecil Andrus, who was secretary of interior in the Carter administration, is running for governor again. Alaska's former Gov. Walter Hickel, also a former secretary of interior, is among a wide field in that state's GOP primary. Former governors lost primary bids in Alabama, Arkansas and South Dakota.

One reason for the large number of rematches may be that 1986 is an off- year election in the sitting president's second term - a time when both parties may feel they have a good chance, said James Shenton, a Columbia University history professor specializing in the nation's governors.

''Rematches tend to be usual when everyone feels there's a good chance of winning,'' he said.

Of the five rematches, three are by Republican challengers, and one Democratic leader contends that reveals a shortcoming in the GOP's ability to field good candidates.

''I see it as a manifestation of a basic problem of the Republican Party - basically they are a top down party,'' said Charles H. Dolan Jr., executive director of the Democratic Governors' Association. ''They don't have the farm teams we do, candidates running for city council, state legislatures and other state offices.''

He also pointed to the advanced age of some, such as Clements, at 69, and Rhodes, who at 76 is such an established figure there is a statue of him on the capital grounds in Columbus.

''Their candidates, I call them retreads, are pretty much over the hill,'' said Dolan.

Republicans dispute that view, and Ms. Davis said the job of governor, with its patronage and other powers, is just so attractive some former governors can't walk away from it.

''There's just no better job to have if you want to be a real political player,'' she said.