District officials are bracing for a surge in the number of students requesting free tutorial services under the federal No Child Left Behind Act, with low-income children at nearly half of the city's public schools now qualifying for the aid based on the schools' failure to meet test-score benchmarks.

But officials expressed concern yesterday that there may not be enough money to provide the federally funded tutoring to all who are entitled to it.

Test results released Monday revealed that of 149 assessed city schools, 68 schools are deemed as needing improvement, up from 15 last year. The 68 schools were placed in that category because for two years in a row, they did not make adequate progress in raising scores on the Stanford 9 reading and math exams.

The designation means that students at those schools are entitled to transfer to other schools and, in the case of low-income children, to demand free after-school tutoring.

But school officials have said there are not enough spaces in higher-performing schools to accommodate all the children who qualify for transfers. And yesterday they said the tutoring option may also be problematic.

The city receives $5.6 million in federal funds each year to pay for the tutoring services. Last school year, slightly more than 2,000 children participated, at a cost of $1.3 million. Although money left over from last year has been rolled over to this year's tutoring budget, it may still not be enough to cover the expected increase in demand, said Wilma F. Bonner, who oversees the school system's use of federal grants.

"If you do the math, the funds are not there to provide services for every child," Bonner said. "The numbers say that $5.6 million is not enough."

The school system was able to pay for tutoring for all eligible students whose parents applied last year, and it has budgeted an average of $1,570 per child, which pays for roughly 45 hours of tutoring per school year. At that rate, $5.6 million would pay for tutoring for about 3,600 students.

That is a fraction of the 33,000 students who are enrolled in the 68 schools. Officials said they are not certain how many of the students meet the income guidelines for the free tutoring, but they acknowledged that the school system may have to give priority to students with the lowest test scores.

The first round of applications for tutoring will be due Sept. 6. "Then we can gauge if we have to enforce a priority-service model," Bonner said.

This week, the school system began mailing packets to all parents and guardians of the 33,000 students at schools needing improvement.

The packets explain their options under the 2001 No Child Left Behind law and include a list of the 27 private organizations that have been selected to provide tutoring in reading, math and the use of technology for schoolwork. Most of the tutoring is given after school or on Saturdays and takes place in the schools where the students are enrolled. Parents can choose among the providers.

Officials also said that each elementary school deemed as needing improvement will have two designated schools to which its students can transfer. But at the middle and junior high school levels, there is only one school that will accept transfer students: Thurgood Marshall Educational Center in Northeast Washington, which has students from pre-kindergarten through the eighth grade.

For high school students, there is no school that will automatically accept transfer students. Twelve of the city's 15 traditional high schools are now classified as needing improvement, and the others are magnet schools with special admissions criteria.

"The information in the packets says very clearly that at the high school level, there are no schools for the youngsters to transfer to," Bonner said. The packets encourage parents of high school students to apply for tutoring. They also contain information about charter schools and the city's federally funded school voucher program.

Parents who want to transfer their children to another school must apply in person at the Thomson-Logan Building, 215 G St. NE. Applications will be accepted from Monday through Aug. 21, from 8:30 a.m. and 4:30 p.m. weekdays and from 9 a.m. to 1 p.m. on Saturdays. Principals at the 68 schools also will hold briefings for parents about their options next week.

In interviews yesterday, parents of students at some of the 68 schools expressed concern, but little surprise, about the schools' status.

"It's very disappointing, but it's not a shock," said Laraysha S. Shaw of Southeast Washington, whose son Juan Cartledge recently graduated from Ferebee-Hope Elementary School. Juan is supposed to enroll at Hart Middle School in the fall. Both schools have been designated as needing improvement.

In the spring, Shaw applied to have her son attend Stuart-Hobson Middle School in Northeast or Hardy Middle School in Northwest. Both schools have waiting lists. Although Stuart-Hobson is also classified as needing improvement, Shaw said she believes it is still a better school than Hart. She is considering applying for Juan to receive tutoring in reading.

Wanda S. Morsell of Southeast Washington transferred her daughter Kia last year from Sousa Middle School to Stuart-Hobson.

Even though Stuart-Hobson is classified as needing improvement, Morsell intends not only to keep Kia there, but also to transfer her other daughter, Tia, there. Kia will enter the seventh grade, and Tia the eighth.

"You can't keep running," Morsell said. "At some point, you're going to have to stand up and fight for the school your kid is at. I want to fight for resources for that school."