HIGH ON the list of troubles no one wants to deal with are teen-age criminals -- the sort of tough young people who hop around the streets mugging others while being unemployed and refusing to go to school. In Washington, many of these youths end up at the city's detention centers, Cedar Knoll and Oak Hill, in Laurel, Maryland, 30 miles from the city. Children found by courts to be involved with crime are held in those places. Mixed in with them, for an average of 70 days, are children merely accused of crime -- most of them are subsequently found not guilty.

In 1978 Judge Gladys Kessler, after studying reports of suicide attempts, sexual abuse and beatings at the centers, demanded immediate improvements in staffing, education, medical care and other services.Her ruling is still under appeal. Meanwhile, few of her recommendations have been acted on.

Last December conditions at the centers again came to her attention. A 12-year-old robbery suspect at Cedar Knoll claimed he and three others had been beaten by a counselor whom he had accused of having sex with another boy. The 12-year-old said older children had beaten him up and lit matches stuck between his toes as he slept. Said Judge Kessler: "The District government is prepared -- quite literally -- to give up on this child and warehouse him at Cedar Knoll where he has already been abused by a counselor, where he will get minimal schooling and where he will get little or no counseling or therapy."

A visit to Laurel confirms much of what the judge said. The counselors do not appear to be bad guys so much as men caught in a brutal situation. "It should be one of us to every 10 of them," a counselor says, "but it's one to every 20. Suppose you're locked up with 20 of these kids, three of them have got a murder beef. All of them want to try you. If they were coming at you, you'd do anything you could to keep alive, too. Is that brutality?"

Around the centers are yellow complaint boxes. In 1980 there were 2,000 complaints, 200 for beatings. Yet no counselor was fired. Even in a case where a child's jaw was broken, the counselor found to be involved appealed and was reinstated.

Vocational shops at Oak Hill are closed: either teachers do not want to deal with these teen-agers, or positions have fallen to a budget freeze. Academic classes are regularly canceled because, though money is available, substitute teachers can't be found. Academic schools at the centers are not connected to District schools, so children, typically four years behind in reading and math when they arrive, often drop out when they return to the city. "School ain't nothing out here," says a 17-year-old accused bank robber at Oak Hill. "I ain't been in weeks. The only shop they got me in is laundry. That ain't teaching me nothing. They just got me doing their laundry."

The dominant philosophy at the centers is keeping the teen-agers locked up so they won't be on city streets to bother anyone. Administrators, judges and counselors at Laurel admit that rehabilitation is a foreign concept. But without rehabilitation, the ideal of the juvenile justice system acting as a wise elder leading youngsters away from crime is a mockery. The juvenile system becomes a punishment system alone. An estimated 25 percent of the children come back to the centers, charged with another crime, and an even higher percentage moves on in time to adult jails.