The abandonments began Sept. 1, when a mother left her 14-year-old son in a police station here.

By Sept. 23, two more boys and one girl, ages 11-14, had been abandoned in hospitals in Omaha and Lincoln. Then a 15-year-old boy and an 11-year-old girl were left.

The biggest shock to public officials came last week, when a single father walked into an Omaha hospital and surrendered nine of his 10 children, ages 1 to 17, saying that his wife had died and he could no longer cope with the burden of raising them.

In total last month, 15 older children in Nebraska were dropped off by a beleaguered parent or custodial aunt or grandmother who said the children were unmanageable.

Officials have called the abandonments a misuse of a new law that was mainly intended to prevent so-called Dumpster babies - the abandonment of newborns by young, terrified mothers - but instead has been used to hand off out-of-control teenagers or, in the case of the father of 10, to escape financial and personal despair.

The spate of abandonments has prompted an outcry about parental irresponsibility and pledges to change the state law, which allows caregivers to drop off children without fear of prosecution.

But it has also cast a spotlight on the hidden extent of family turmoil around the country and what many experts say is a shortage of respite care, counseling and especially psychiatric services to help parents in dire need.

Some who work with troubled children add that economic conditions, like stagnant low-end wages and the epidemic of foreclosures, may make the situation worse, adding layers of worry and conflict.

"I have no doubt that there are additional stresses today on families who were already on the margin," said Gary Stangler, director of the Jim Casey Youth Opportunities Initiative in St. Louis, which aids foster children entering adulthood.

Mark Courtney, an expert on child welfare at the University of Washington, said that what happened in Nebraska "would happen in any state."

"These days there's a huge void in services for helping distressed families," Courtney said.

When children are abused or neglected, they can be taken by the child-welfare system, and possibly enter foster care. When they commit crimes, they enter the juvenile justice system. In both cases, children and parents are supposed to receive counseling and other aid.

But when troubled children do not fit those categories, they often fall through the cracks, Courtney said.

Even middle-income families with health insurance often have only paltry coverage for psychiatric services and cannot afford intensive or residential treatment programs. The poorest, on Medicaid, often have trouble finding therapists who will take the low rates.

In July, Nebraska became the last of the states to enact a safe-haven law. Such laws permit mothers to leave an infant at a facility with no fear of prosecution.

Nationwide, more than 2,000 babies have been turned over since Texas enacted the first such law in 1999, according to the National Safe Haven Alliance in Virginia.

But Nebraska's version was far broader than all others, protecting not just infants but also children up to age 19.

State Sen. Arnie Stuthman, sponsor of the Nebraska bill, said some legislators had said they wanted to protect all children from harm.

"The law in my opinion is being abused now," said Stuthman, who said he would push for a revision.

"There are family services out there, but some people may lack the resources to take advantage of them, and we've got to take a hard look at what more we can provide."

Todd Landry, the state director of children and family services, denied that the involved families had not had access to aid - most of the children, for example, were in the state Medicaid program and some had received psychiatric care - and he noted that well-publicized hot lines could direct families to help.

"Some parents had accessed our services but weren't getting the results they wanted," Landry said.

"The appropriate response is to reach out to family, friends and community resources," he said. "What is not appropriate is just to say I'm tired of dealing with this and drop the child off at a hospital."

Landry said parents and guardians were mistaken if they thought they could walk away from their responsibilities. For now, such children will be placed in foster care or with relatives, but the courts could require parents to attend counseling and might even order them to pay child support.