A school custodian, Robert G. Rodrigue, said that although he had not been critical of the Mayor's job performance, the child-support case was starting to tarnish the city's name.

About 644,000 child-support cases were in arrears last year, a spokeswoman for the agency said.

Robert Parish, starting center for the Boston Celtics, has been fined $5,000 for missing court appearances in a child-support case in Oakland, Calif.

Crackdowns Are Growing New Jersey, with some 300,000 child-support cases, does not keep figures on the number of arrests for nonpayment of child support, said Mr. Rainville, the courts official.

Nearly one-third of all child-support cases involve parents and children in different states.

Over the last five years, she said, the number of child-support cases handled by the division has risen by 125 percent.

He seemed the ideal person to answer the basic question raised by the child-support case: Are Mr. Perelman and Ms. Duff going to hell?

Because the states are the primary authorities in child-support cases, the executive order that Mr. Clinton will sign simply gives the Federal Government stronger tools for its supporting role, Administration officials said.

In New Jersey, we have more than doubled child-support collections for A.F.D.C. families within the last five years, but still 85 percent of our child-support cases are in arrears.

With the help of the center, she won a child-support case, but she said she is still having problems getting money for her sons from their father.