On January 2, filing closed for the District of Columbia’s April 1 primary. The District has four ballot-qualified parties, all of whom nominate by primary. There are four city council seats up in 2014 from particular districts. The only parties that have candidates for any of the district seats are the Democratic Party and the Libertarian Party. Although members of the Republican and Statehood Green Party have candidates for the at-large seat, they have none for any of the district seats.
The D.C. Board of Elections web page lists the primary candidates here. See the list of candidates on the right, near the top.
It is always possible that write-in candidates in the primaries will win a party nomination.