WASHINGTON is developing into an area with a central city occupied by the very rich and the very poor, while its suburbs sort out according to who is single, who is married and who has children. Those findings are contained in a provocative report by the Greater Washington Research Center. If it's right, both city and suburbs face qualitatively new decisions soon. For the District, it will be what to do with the clusters of poor people squeezed to the edge of the city.For the suburbs, it will be how to keep a political system vital when people are moving across jurisdictional lines more frequently than in any other metropolis in the country. The constant motion keeps people from moving up in the area's political system, and a growing number of childless people are not entering the political system at all.

According to the research center, the change in the District arises from an influx, mostly from outside the area, of young and single well-to-do people. This group is pushing inner-city poor people to the far reaches. Middle-clas families, meanwhile, are leaving for the suburbs, taking their incomes and children with them. They are often black -- one out of every eight suburban families is now black -- and though they make their own demands for services, they contribute substantially to the area's tax base.

The near suburbs are becoming an extension of wealthier parts of the city. In Arlington and Alexandria, 72 percent of the households now have only one or two persons. But generally the suburbs remain a place for families, and those families move surprisingly often. In 1977, about a quarter of the Washington area's families changed residences and half of them crossed into new jurisdictions. The traffic was heaviest in Alexandria and Fairfax.

For most suburban jurisdictions, all of this is good news of a sort. The poor people whom the suburbs are wary of are not pushing in, overrunning the schools and "changing" neighborhoods. But as the city becomes increasingly a preserve for rich and poor, middle-class people will be less able to move back in. As a result, they may become all the more protective of their suburbs. At the same time, frequent movement in the suburbs may diminish broad involvement in local government and schools, and may enhance the influence of a relatively small number of stable people.

The area's major challenge will be the poor people at the edges of the edges. They want for jobs and adequate housing and they need costly public services. Whether they are ignored or tended to properly, their problems will touch city and suburbs alike.