In the District, politics is in its infancy. But in at least one instance, the city has moved into turbulent adolescence. More women candidates are running for public office than in most other cities around the country.

It's exciting--and right on target--that women are beginning to assume leadership roles. In his book "Changing of the Guard--Power and Leadership in America," political journalist David Broder found that current leaders in business, industry and government who share the experience of World War II and the Great Depression will be passing on in the next decade. A vacuum will be created for a whole new crop of leaders--more women, minorities, and people from the South and suburbs. In a word: diversity.

It's happening nationally as well as locally. "It is clear we have thousands of women who are running--both Democrats and Republicans--in l982," says Landis Neal of the Democratic National Committee Women's Division. "In large part, it is due to the politicization of women who have been working for certain causes . . . and have learned the political process."

Being a woman is still a negative in some places, but it isn't in Washington. Half the City Council is female, for example, and a good potential leadership pool exists.

But I'm a little worried as I think of the future and the challenge. How will women seize these leadership roles? For if Washington women are ahead of the game in starting now to prove what they can do, some of their successes and failures, problems and solutions are case histories of the challenges of budding leadership.

There is no common thread that unites the dozen-plus women who have filed in party primaries for every city office, unless it is they have a tougher time raising money on the local level. Many are strong candidates and proven vote-getters. They range from superstar Patricia Roberts Harris, incumbent Marion Barry's main rival, to candidates with low name recognition but good ideas, like real estate agent Patricia Wells, a Democrat, who is seeking an at-large seat on the City Council against such well-known figures as incumbent Betty Ann Kane and school board member Barbara Lett Simmons.

Some of the women are soft-spoken but gutsy like Harvard-trained Marie Dias Bembery, fighting to get back on the ballot as challenger to D.C. Del. Walter E. Fauntroy. In a hands-on-the-hip manner, when she can get somebody to listen, she'll go for the jugular: "Fauntroy's most glaring fault is his lack of follow-through. He is good with catchy phrases but once you get beyond this, where is the substance? It's rhetoric. I reject that kind of so-called leadership. I also reject his singing."

Others are experienced professionals like Charlene Drew Jarvis, whose most glaring problem is that she decided to run for mayor four years too soon, and Marie Nahikian, the Ward 1 Council candidate who gained a reputation in the housing struggles in Adams-Morgan.

The predictable mumblings about problems within the political camps are exacerbated when the candidates and those around them are primarily women, and some of this year's female candidates have had their problems. Patricia Harris has had three press secretaries since she announced her candidacy, the most recent resigning earlier this week. This kind of upheaval would seem to be the last thing you would want in a campaign when many people question still question whether women can exercise leadership anyway. Patricia Wells is still looking for an issue on which to focus. The elections board ruled that Marie Bembery didn't file in time to get on the ballot. Others lack the skills they need to increase their low name recognition.

One of the problems is that few of the women running for office or their staffs have been truly groomed for leadership. Others are at a further disadvantage because they haven't learned to make use of that network of political friends and connections that has advised and sustained male candidates for years.

There are exciting chances for these newcomers in a hardball game despite the inevitable growing pains. The opportunity is to exercise leadership and real power and be more serious about work and service than about tramping in the same old power footprints some of the men left behind. It would be a shame to blow it.