In the last few years, women members of the U.S. Senate have attained greater numbers and growing prominence.

Of 13 women senators, several have become influential public figures, including Republican Kay Bailey Hutchison and Democrats Dianne Feinstein and Patty Murray. And if Republican Elizabeth Dole joins Democrat Hillary Rodham Clinton after November, the Senate will have two women often touted as national candidates.

But more significant may be the high number of women winning governorships. After all, four of the past five presidents have been governors.

And the number of women governors may take a big leap forward this fall over the five who now govern Arizona, Delaware, Montana, Massachusetts and New Hampshire.

In several states, the prospects for women gubernatorial aspirants will be influenced heavily by primary results, either in her own or the opposition party.

In Kansas, for example, state Insurance Commissioner Kathleen Sebelius, the daughter of one-time Democratic Gov. John Gilligan of Ohio and the daughter-in-law of a former GOP House member, awaits the outcome of a GOP primary battle to succeed term-limited Republican Bill Graves.

And in Hawaii, Republican Linda Lingle, a narrow loser four years ago, awaits a confused Democratic battle in which two potentially strong foes have withdrawn.

Both may be fall favorites.

Elsewhere, women candidates, mostly Democrats, face their own multicandidate primaries.

The best known, former Atty. Gen. Janet Reno, leads attorney Bill McBride in the race to face Florida GOP Gov. Jeb Bush. But the polls also indicate Reno might be a weaker candidate against Bush than McBride.

In Massachusetts and Michigan, women Democrats are making strong bids against male rivals.

In Massachusetts, state Treasurer Shannon O’Brien’s four male foes include former Labor Secretary Robert Reich. The winner faces a fight against Republican Mitt Romney.

And in Michigan, state Atty. Gen. Jennifer Granholm has two prominent male rivals, former Gov. Jim Blanchard and former House Minority Whip David Bonior. Polls show she would have the best chance against the GOP.

Women also have a chance of winning Democratic nominations in New Hampshire, where state Senate Democratic leader Bev Hollingworth hopes to succeed Gov. Jeanne Shaheen, and Rhode Island, where Myrth York hopes her third race for governor will be the charm.

In Arizona, state Atty. Gen. Janet Napolitano is favored to win both the Democratic nomination and the governorship now held by term-limited Republican Jane Hull.

Several women Democrats are unopposed for gubernatorial nominations. The most likely winner is Maryland Lt. Gov. Kathleen Kennedy Townsend, the eldest child of the late Robert F. Kennedy. Townsend’s GOP rival is Rep. Robert Ehrlich.

Two others will have uphill fights against well-known Republican rivals. In Alaska, Lt. Gov. Fran Ulmer probably will face veteran Republican Sen. Frank Murkowski. In Arkansas, state Treasury Jimmie Lou Fisher is an underdog to Gov. Mike Huckabee.

In Georgia, Republican Linda Schrenko, state school superintendent, would face an uphill battle, if she wins the primary, against Gov. Roy Barnes.

Whichever women are elected will join holdover Govs. Ruth Ann Minner of Delaware, a Democrat, and Judy Martz of Montana, a Republican. Their growing clout may bring closer the day when a woman is picked again for her party’s national ticket, perhaps in 2004.