Two women are vying for the Republican gubernatorial nomination in Tuesday's primary election, and the winner most likely will face Democratic Gov. Mike Sullivan. The GOP candidates are Mary Mead, daughter of former Gov. and U.S. Sen. Cliff Hansen, and state Rep. Nyla Murphy. Mead, a Teton County rancher, and Murphy, a 12-year state representative from Casper, seemed to agree on issues more often than not during the primary campaign. Both support abortion rights, oppose other states dumping garbage in Wyoming, and favor the death penalty. Where they differ is on Mead's call for a cut in minerals taxes to spur exploration. Murphy believes the current tax system is adequate and that the economy will improve under the state's diversification efforts. Sullivan is seeking his second term. His opponent for the Democratic nomination is Ron ``Suds'' Clingman, a Rock Springs motorcycle repairman who believes his stances on lowering the drinking age back to 18, legalizing gambling, and cutting the salaries of public officials are popular. U.S. Sen. Alan Simpson, the Senate Minority Whip, is seeking a third term, and U.S. Rep. Craig Thomas is pursuing his first full term in office. Simpson faces two political unknowns in the GOP primary, while six unheralded Democrats are seeking their party's nomination for the seat. Thomas was appointed to fill Dick Cheney's unexpired term in office when he was appointed defense secretary last year. Thomas is unopposed in the primary as is his Democratic opponent, Pete Maxfield.