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Neither of the nation's two largest cities, New York and Los Angeles, have ever had female mayors, but that could change big time this year, as both cities have strong female candidates with a chance of becoming mayor, in races where the incumbents are term-limited.

2013 could be a "year of the woman" in major city halls, in what women's political groups are hoping will build momentum toward an even bigger win in 2016. If that happens, it could start this week, with developments in both of the high-profile races.

Los Angeles' mayoral runoff election will be Tuesday, with a tight contest pitting Councilman Eric Garcetti and City Controller Wendy Greuel.

Recent polling by the Los Angeles Times gives Garcetti a narrow lead, though with a sizeable chunk of undecided voters still in play. The race has shattered city spending records, with Greuel's financial disadvantage made up by for by a pro-Greuel Super PAC backed by public-employee unions.

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New York City will elect a new mayor Nov. 5. The primary - and the Democratic primary is probably the ballgame - is in September, with a runoff between the top vote-getters triggered if neither candidate gets 40 percent of the primary vote.

City Council President Christine Quinn is the frontrunner in a crowded field to replace Mayor Michael Bloomberg. Quinn would also be the first openly gay mayor of New York.

That race could get a whole lot more interesting this week, with former Rep. Anthony Weiner widely expected to declare his candidacy. Last week, reporters caught Weiner filming a video in front of his home, apparently to announce his run. (Of course, he's been the subject of far less presentable self-portraits, in images he sent to several women before his political demise in 2011.) If he's the final candidate standing against Quinn, gender politics won't be far from that race.

Also of note, Houston, the nation's fourth-largest city, is the largest to be led by a woman: Mayor Annise Parker. Parker is up for reelection in what would be her final two-year term in November.