More students than expected showed up in some Virginia schools this fall, sending administrators scrambling to find funds to educate them.

In Alexandria, 200 more students than the 9,729 predicted were enrolled in classes. In Fairfax, school officials expected 129,144 students, but by early September 130,401 already had enrolled. School officials in Arlington say they enrolled 300 more students this year than the 14,481 anticipated.

School officials in Arlington and Fairfax counties said new teachers have been hired to teach the new students, although it is not yet clear where the money will come from to pay for the additional staff.

Arlington schools spokesman David Rorick said the county will fall about $1.4 million short in its current school budget, with about $1 million of that directly attributable to higher school enrollments this year. It cost about $7,838 to educate a student in the county last year.

The increased expenditures come at a time when the school budgets in most localities already have been slashed, and when state and federal contributions to education are on the decline.

"If the financial situation weren't so tight, we'd go back to the county and ask for more money," Rorick said, "but there's nothing there. Everything's been slashed to the bone."

School officials in Fairfax County say they hope to absorb the extra students more easily because of the size of the school system. Nevertheless, they say the hiring of additional teachers will cause a strain in the wake of this year's budget cuts, and even more drastic cuts expected in the coming school year.

In Montgomery County, school officials said 1,154 more students attended school this fall than the 103,772 anticipated.

Demographers attribute much of the disparity between their projected figures and the actual school enrollments to growth in the size of Washington area households, a trend they say is likely to last through the end of the decade.

"It's going on all over the country, particularly in the large metropolitan areas: More kids are turning up in the schools than anticipated," said George Grier, a demographer and senior consultant with the Greater Washington Research Center, a nonprofit group.

In the Washington area, Grier said, much of that new growth is concentrated inside the Capital Beltway.

"Desirable inner suburban jurisdictions are getting an influx," said Grier, adding that the greater affordability of homes nearest the District is attracting large numbers of young families with children.

School administrators inside and outside the Beltway, however, also say that faster-than-anticipated growth in the immigrant population is a major factor in the shortfall of enrollment projections.

"Most of the difference is from kids who are not from this country," said Gary Chevalier, a coordinator in the planning office for Fairfax County schools who, like other school administrators, said that most of the increase occurred at the grade school level.

In Alexandria, the increase in the number of Hispanic students in recent years has been offset by declines in the numbers of black and white students, said James Akin, executive assistant to the superintendent.

"That did not take place this year," Akin said. "Those two groups appear to be stabilizing, while the Hispanic group continues to grow."

The fact that so many of the new students come from other countries compounds the problem of large enrollments, Rorick said.

"On top of the higher numbers, it will be more expensive to educate them," he said. "It's a double whammy."

In Montgomery County, class size will grow by an average of one student per class, because a hiring freeze prevents adding teachers.

"All of the students will be absorbed within our current budget," said Brian J. Porter, a spokesman for the Montgomery County schools.

"We have schools that are filled to the brim," Porter said, "but we are not seeking funding for additional teachers because the money isn't there."

In Virginia, part of the extra cost will be taken care of by the state, which allots its school funding on a per-pupil basis.

But school officials in Virginia say the additional state funding isn't expected to arrive until June, and will cover only about 20 percent of the unexpected expenses.

"The money from Richmond will not cover our increased costs," said Rorick said, who estimated that Arlington can expect to receive about $200,000 from the state.

The school enrollment projections are based on mathematical formulas determined by a school system's past enrollment patterns. In geographic areas where there is rapid development, demographers also factor in the number of students each new housing unit is likely to yield.

But forecasting the numbers of students who will enter school each September can be especially tricky in the Washington area, school officials say, with its high number of mobile federal workers and military employees.

"It ebbs and flows," said John Peterson, director of pupil accounting for the Prince George's school system. "A new resident manager may move into an apartment complex, and the school enrollment in the area can go down, because he doesn't allow tenants to double up."

In Montgomery County, Porter said, revising downward a projection that county officials deemed to be too high permitted them to allot less money for the school year, "which essentially amounted to a budget cut," Porter said. "The county decided it was prudent to be financially conservative, but school officials predicted the higher enrollments."