Bea, 16, can rattle off the mental institutions she has been in since she was 12, the way some teen-agers tell you about the summer camps they've attended.

Likewise, Bill, also 16, coolly recites the details of his 6-year-old arrest record: breaking and entering, drunk in public, driving without a license, tampering with vending machines, possession of burglary tools and trespassing.

For these two Prince William County youths, the latest stop in their troubled lives has been at Different Strokes, an alternative educational program for youngsters with emotional, learning or legal problems run by the county schools and the county mental health board.

Bea and Bill are among 21 students who receive personalized instruction and psychological counseling at Different Strokes, which opened five years ago in a split-level house in Manassas and expanded this year to a second facility in a Dale City church. For the first time in their lives, these two teen-agers say, they show up regularly for classes, are making substantial academic progress and are being helped by a devoted teaching staff.

But if the Prince William County school board sticks to a decision it made earlier this month, there won't be a Different Strokes for these students in September. The board voted to eliminate the $126,000 budgeted for Different Strokes and to return students in the program to other special education classrooms or private institutions when the new school year begins next fall.

Last week, dozens of students' parents and teachers pleaded with the board to reinstate the program. After two emotional town meetings, several board members agreed to take another look at Different Strokes, where instructors claim that 87 percent of the students find jobs or successfully move on to less structured academic or vocational classes.

"I'm really shocked they cut out the whole program, when just a year ago I was before the same board looking for a second program and it was approved," said Paul Borzellino, director of Different Strokes.

The decision to drop Different Strokes came after the county Board of Supervisors told the shcool system to cut $4.8 million from its $102 million budget proposal for the coming fiscal year. The county mental health board also contributes $107,000 to Different Strokes, but mental health officials say that while they can continue to offer therapy to students and their families, they cannot run a full educational program without support from the school system.

Superintendent Richard Johnson said Different Strokes' was cut because it is an expensive program that serves only a handful of the county's 35,000 pupils. In making the budget cuts -- ordered because of a loss of federal and state revenues and an austerity drive by the supervisors -- the school board's top priorities were to preserve the regular kindergarten through high school program, give staff members a 9 percent pay increase and avoid laying off as many employes as possible, Johnson said.

"I have very mixed emotions about this, said school board Chairman Gerard Cleary. "I think it's been a very viable program and it has a very good track record. But somewhere along the line we have to set out priorities. I'd like to keep it, but it comes down to dollars."

While school officials insist they would have to sacrifice another program, such as driver education to pay for Different Strokes, some teachers speculate that the board decided to cut the special school as a sympathy ploy to get more money from the supervisors.

If so, the tactic may have worked. Supervisors' Chairman Kathleen Seefeldt said she is against dropping Different Strokes, and if the school board comes back and asks the supervisors for extra money to keep the program, she thinks the supervisors will say yes.

If Different Strokes is abandoned, many of the students will be placed in classes for the emotionally disturbed or learning disabled in the county's other high schools, Johnson said.But supporters of Different Strokes reject that plan, arguing that the students are in the alternative school because they couldn't make it in traditional classrooms.

"If you close the school down now, we'll all be back on the streets," a tearful Bea told the school board last week. Bea started attending Different Strokes last winter after she attempted suicide, and she believes she will wind up in a psychiatric hospital again if the program is canceled.

The school board acknowledged that some youngsters probably will be sent to private hospitals or residential schools, but as of last week, no figures were available on how many students would need this care. Under federal law, the school system is obligated to pay tuition for students with problems who can't attend public schools. County mental health board chairman Robert Holley estimated it would cost about $18,000 per student per year at a private institution. Multiplied by 21, the number of students now at Different Strokes that comes to $378,000 or $125,000 more than the combined school-mental health board budget that had been proposed for next year.

"It is a false economy to close a school like Different Strokes, only to force parents to send their children to other institutions at great expense to the county," said Paul Watson of Manassas, whose emotionally disturbed son entered Different Strokes last fall after a year at a private school outside Philadelphia, which cost the county $1,400 a month.

Other supporters of Different Strokes argue that the larger expense is the long-range cost to society if troubled youngsters do not get help early.

"Emotionally disturbed children grow up to be emotionally disturbed adults who take potshots at presidents," warned Mary Blanks of Dumfries, whose 19-year-old son is finishing school at Different Strokes. "If you don't help them now, we'll all pay more in the long run. We'll pay in court costs, for probation officers and the costs of incarcerating them."