Republican Nancy K. Falck yesterday became the first member of the Fairfax County Board of Supervisors formally to announce for reelection in this fall's elections.

The announcement by Falck, who represents the Dranesville District that includes McLean and Great Falls, had been expected.

Falck, a former school board member who was elected to her first four-year term in 1979, does not anticipate a difficult reelection battle this November. So far no challengers have emerged, she said, adding, "at least not that I know of."

All nine seats on the board are up for reelection this year and all of the incumbents are expected to seek reelection. The board currently is controlled by the Democrats, who hold five seats, but Republicans are expected to mount serious challenges in at least two disticts.

Democrats Sandra L. Duckworth and James M. Scott, and Republican Marie B. Travesky generally are viewed as the most vunerable incumbents. Supervisors with stronger relection prospects include Democrats Joseph Alexander, Martha V. Pennino and Audrey Moore, and Republicans John F. Herrity and Thomas M. Davis.

Falck said that, if reelected, she will work for "affordable housing for our children, so that when they mature they will not have to leave the county to buy a home."

Other projects to which she would give priority, she said, include programs for senior citizens, efforts to encourage businessmen to offer more day care services, and projects to relieve congestion at Tysons Corner.