The impact of two emotional issues of the past - school busing and radicalism - will be tested today in mayoralty elections in California and Wisconsin.

Voters in nine U.S. cities with more than 100,000 population will elect mayors, but the nationwide attention is focused on Los Angeles and Madison.

The school busing issue has been exploited in Los Angeles by state Sen. Alan Robbins, one of 11 candidates challenging Mayor Tom Bradley. Bradley, a former police lieutenant, is a black in a city where blacks are a distinct minority. Los Angeles' public schools are under a court desegregation order that could require crosstown busing.

In Madison, Mayor Paul Soglin, 31, is being challenged by Anthony Amato, 25, who contends that Soglin's reputation as a radical gives Madison a bad name. Soglin has traveled twice to Cuba during his second term and Amato has made an issue of it during the campaign.

Elections also will be held today to fill the seats of two congressmen who accepted posts with the Carter administration.

In Atlanta, Wyche Fowler Jr., president of the city council, will face John Lewis in a runoff to fill the vacancy created by the appointment of Andrew Young as U.S. ambassador to the United Nations.

Both candidates are Democrats but differ on common site picketing and repeal of right-to-work laws, which Lewis favors and Fowler opposes.

Fowler, a white, led in the primary election and is favored today. Both he and Lewis, a black who formerly headed the Voter Education Project, have strived to keep racial issues out of the campaign, but some blacks have stressed the importance of keeping a black as congressman. The district is 57 per cent white and 43 per cent black.

For Washington State's 7th District seat, vacated by Brock Adams when President Carter named him Secretary of Transportation, voters will narrow a field of 25 candidates down to two for a runoff election May 17.

Democratic favorites to make the runoff include Martin Durkan, a vetera politician who has twice run for governor, and Marvin Durning, an environmentalist who lost to the state's new governor, Dixy Lee Ray, in the Democratic primary in September.

The leading Republican candidates appear to be state Sen. Jack Cunningham and Norward Brooks, former Employment Security Department commissioner.

The most emotionally divisive campaign has been in Los Angeles, even though Mayor Bradley is favored to avoid a runoff by winning more than 50 per cent of today's vote.

Nonetheless, Bradley has been placed on the defensive by Robbins, who has called for a referendum on allowing communities in the predominantly white San Fernando Valley to withdraw from Los Angeles.

One Robbins television ad shows a school bus with a voice saying: "Now they're telling us our kids have to go to school 20 to 30 miles away." Then Robbins comes on, saying: "I am against forced busing. It's bad for our children. It's bad for our community."

Bradley, responding to the aggressive Robbins campaign, has opposed "massive crosstown busing" but said he will abide by any court integration order.

Both Bradley and Robbins are Democrats, and the election is ostensibly nonpartisan. However, Robbins has been receiving campaign assistance and funds from Republican political activists.