A tight race between a veteran woman politician and an outspoken moderate from Mississippi's stormy past is shaping up for Tuesday's runoff for the Democratic gubernatorial nomination.

If Lt. Gov. Evelyn Gandy beats lawyer William Winter, she has an excellent chance of becoming Mississippi's first female governor in the November election.

This has been the calmest race in memory; mud slinging has been absent.Winter has stressed the need for professionalism in office while Gandy has stressed her 30 years' experience in state government.

Neither Gandy, a former aide to an outspoken segregationist, the late Sen. Theodore G. Bilbo, or Winter wants to dredge up the past. Winter lost races in 1967 and 1975 because of a "liberal" tag. Gandy has deleted Bilbo's name from her campaign biography. The black vote was split equally in the primary, and both need a sizeable chunk of it to win Tuesday's runoff.

There has been no overt discussion of gender but the message is clear in the "tough enough" theme of the Winter campaign. Winter, a bookish Jackson attorney, is pictured firing his pistol at target practice in his TV spots.

Gandy is employing her usual low-key campaign. Her forte is the one-on-one encounter, and her organization is almost nonexistent. This year, for the first time, she was persuaded to hire a Washington-based political strategist to coordinate her shoe-string campaign. It was this kind of campaign that put her first in a field to six challengers in the primary.

Winter's campaign, with telephone banks and pollster Peter Hart, is more sophisticated. Washington consultant Bob Squier is devising strategy.

Winter is traditionally weak in rural areas. He spent last week campaigning in the country. Gandy, whose appeal is strong among rural voters and professional women, campaigned in towns.

The winner of the Democratic runoff will face Republican Gil Carmichael, a Meridian auto dealer.