CHEYENNE, WYO., AUG. 22 -- The rancher daughter of a former Wyoming governor won the Republican nomination for her father's old job Tuesday and will square off in November against Gov. Mike Sullivan (D), who coasted to victory.

Senate Minority Whip Alan K. Simpson (R) handily won his race for renomination.

With 96 percent of the vote counted, rancher Mary Mead had 67 percent to 33 percent for 12-year state Rep. Nyla Murphy.

"We're not celebrating yet, but we are looking foward to doing it," Mead said from her Jackson ranch. "We have lots of friends here at my house. . . A friend sent a case of champagne and I hope to break it out and toast victory."

Mead is seeking to give Wyoming its first father-daughter combination in the governor's mansion. Her father, Clifford V. Hansen (R), served one term as governor in 1963-67 before being elected to the U.S. Senate.

Sullivan walked away with the Democratic nomination, receiving 88 percent of the vote against motorcycle mechanic Ron "Suds" Clingman, who had called for lowering the drinking age to 18 and decriminalizing drugs.

Simpson will meet Democratic nominee Kathy Helling, a college student.

Mead's campaign stressed her skills as a rancher and businesswoman and attacked Sullivan's economic development efforts. Murphy accused Mead of having a negative attitude toward Wyoming and of failing to propose solutions to the shortcomings she perceived.

Rep. Craig Thomas (R) had no opposition in the primary. Elected last year to fill the vacancy created by Defense Secretary Richard B. Cheney, Thomas is seeking his first full term in the House. Also unopposed was his challenger, Pete Maxfield (D), a University of Wyoming law professor.