School boards in Fairfax and Arlington counties each decided last night to close an elementary school next year because of declining enrollments in older, more established neighborhoods; the Fairfax board is likely to close two additional schools soon for the same reason.

In Fairfax, school officials decided it will be advisable to close three schools in the eastern half of the county at the same time the county begins building three new elementary schools in the growing, western portion of the county.

As the closing process started last night, the Fairfax board voted to consolidate Lewinsville Elementary into Kent Gardens Elementary in McLean. InArlington, the school board decided to consolidate Woodmont Elementary into Taylor in the northern part of the county.

Parent groups at the four schools, recognizing the likelihood of involuntary closings, had petitioned for the mergers.

The closing of Woodmont in Arlington was controversial nevertheless. Parents of pupils at Key Elementary opposed it on grounds that such moves initiated by PTAs set a bad precedent and that because of attendance district patterns the closing threatens the stability of Key, which has a highly transient, non-English-speaking enrollment. The Arlington school board approved a resolution stating that it will consider only future consolidation proposals as part of a comprehensive plan.

In Fairfax, board members were warned that at least 26 of the county's 120 elementary schools are overstaffed and operating with too few students, making them candidates for consolidations. Although Fairfax, with 123,780 students, still has the largest system in the Washington area, officials estimate that enrollment will drop by about 2,350 over the next two years before leveling off and beginning to increase.

Because of rapid development in some areas of Fairfax, the school board could be considering closings in some neighborhoods of declining enrollment while opening new schools elsewhere, according to Alton C. Hlavin, an assistant school superintendent.

County officials there are eager to avoid the controversy and bitterness that marked the recent closings of 28 Montgomery County schools and 14 of their own in the past nine years.

The two other school consolidations currently under consideration in Fairfax would close Virginia Hills Elementary and send its students to neighboring Rose Hill Elementary and close one of three schools in the Annandale area -- Camelot, Mantua or Pine Ridge elementaries.

Board member Robert E. Frye cautioned against blindly accepting merger requests. "In accepting voluntary action, the group that comes to the board first protects itself from future mergers with communities it may not want to merge with," such as less affluent neighborhoods or areas with large percentages of minorities, he said.

On the list of Fairfax schools proposed in groups for possible consolidation are Bush Hill, Cameron, Cheney, Forestdale, Rose Hill, Springfield Estates, Virginia Hills and Woodlawn in the southern part of the county; Belvedere, Bren Mar Park, Camelot, Chapel Square, Columbia, Mantua, Pine Ridge and Timber Lane in the Annandale/Springfield area; Freedom Hill, Kent Gardens, Lemon Road, Louise Archer, Pimmit Hills and Vienna in the McLean area; and Fairfax Villa, Layton Hall, Westmore and Wood in the Fairfax City and Falls Church areas.