10 Primaries Tuesday

Voters in nine states and the District of Columbia stage the year’s biggest round of primary elections Tuesday, featuring a free-for-all for an open Senate seat in Maryland and the political debut of a new candidate from the Kennedy clan.

Many of the most prominent politicians on the ballots have little or no primary opposition, including Democratic Gov. Mario M. Cuomo of New York and Democratic Sens. Patrick J. Leahy in Vermont and Christopher J. Dodd in Connecticut. Republican senators in similar shape are Alfonse M. D’Amato in New York, Bob Kasten in Wisconsin and Warren B. Rudman in New Hampshire.

Democratic Govs. William A. O’Neill in Connecticut, Madeleine M. Kunin in Vermont, Anthony S. Earl in Wisconsin and Cuomo are unopposed or face only little-known opponents. Rhode Island Republican Gov. Edward DiPrete has no opposition for renomination.

But Minnesota Democratic Gov. Rudy Perpich faces a stiff primary challenge from St. Paul Mayor George Latimer and two other lesser-known candidates, and there is strong competition to fill seats in Arizona and Maryland.

Millionaire Favored in New York

Several states have contested races to pick opponents for incumbent senators, including in New York, where millionaire John Dyson is favored over a former Ralph Nader aide, Mark Green, for the right to take on D’Amato in November.

In Wisconsin, where Kasten is seeking reelection, a recent poll reported more than half the Democrats undecided in a race between front-runners Ed Garvey and Matthew Flynn for the party’s nomination.

In Maryland, Reps. Barbara A. Mikulski and Michael D. Barnes, Gov. Harry Hughes and several little-known contenders are vying for the Democratic nomination to take the Senate seat of Charles McC. Mathias Jr., who is retiring. Linda Chavez, a former aide to President Reagan, is rated the pre-race favorite for the GOP nomination.

Also in Maryland, Kathleen Kennedy Townsend, daughter of the late Sen. Robert F. Kennedy, is favored in a three-way race for the Democratic nomination for a House seat. Townsend, a 34-year-old attorney, is the first member of a new generation of Kennedys to face the voters, with her brother, Joseph Kennedy, seeking a House seat in Massachusetts in a primary later in the month.