Who says there are no second acts in American politics? In an America whose president finally won that office on his third try, political veterans have been winning most of the big primaries in most of the big states this spring. The result is a politics of rematches, a pitting of familiar faces against each other, often over familiar issues.

Example one: Illinois. Amid all the hubbub over the LaRouche candidates and the seven special aldermanic races in Chicago, Illinois voters find themselves faced again with a battle between Gov. James Thompson and challenger Adlai Stevenson. Between them they have run nine times for statewide office over the past 20 years. In 1982 Mr. Thompson won by 5,074 votes out of 3.6 million cast. Mr. Stevenson has the handicap of having to resign the Democratic nomination to 8void being tied to the LaRouche candidate. But another close race seems in store.

Example two: Texas. The governor's race in the third largest state is also a rematch, between Democratic incumbent Mark White and his predecessor, Republican William Clements. Mr. White is a wily politician who has beaten formidable challengers, not only Mr. Clements four years ago but also James Baker in the 1978 contest for attorney general. Mr. Clements, a zillionaire even by Texas standards, spent $21 million in the last two races; this year he says he wants to hold spending to a modest $6 million. He leads in the polls, but his age -- 69 -- may prove a disadvantage.

sk,2 Example three: Ohio. If age is a disadvantage for Mr. Clements, what about Ohio's James Rhodes? He will turn 77 next fall and has been running for public office in Ohio since he was elected Columbus city auditor in 1939. He was elected state auditor in 1952, lost a race for governor in 1954, was elected governor in 1962, 1966, 1974 and 1978, and lost for senator in 1970. In his most recent race for governor, he beat Richard Celeste, the current incumbent, a young whippersnapper, who is now 48. Mr. Rhodes is one of the last of the breed of savvy, earthy Republicans, who knows his way around every corner of the state; he will have Gov. Celeste's handling of the Home State Savings crisis working for him. Most observers presume Ohioans won't elect a septuagenarian governor. But people have lost a lot of money betting against Jim Rhodes.

Why so many rematches? Perhaps because in an era of expensive media campaigns, well-known candidates begin with an edge that is hard to overcome. More important, it's not clear that voters have major complaints against state government, even in states with rocky economies. Some might hold up this year's politics of rematches and old warhorses as a sign that the system isn't working. You could equally plausibly say that the absence of new faces means the voters think they aren't needed.