hen studies last year showed that the share of the nation's children living in single-parent households had declined in the late 1990's, many welcomed the results as signs that the 1996 welfare overhaul was working.

But new research underscores a smaller, unwelcome trend: a rising share of children, particularly black children in cities, are turning up in no-parent households, left with relatives, friends or foster families without either their mother or their father.

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Researchers say they cannot pinpoint the forces driving parents and children apart. But among them, they said, may be the stresses of the new welfare world loss of benefits, low-wage jobs at irregular hours and pressure from a new partner needed to pay the rent.

The findings are helping reopen the debate on what shifting welfare rules are doing to families. They are contributing to second thoughts among some of the most optimistic analysts, even as the White House and some lawmakers are pushing to make the welfare law's work requirements even stricter. The law now requires 50 percent of welfare recipients to work up to 30 hours a week, with some exceptions for hardship.

One important study of census data in each state, recently presented to an audience of welfare experts at Harvard, concluded that among those most affected by the welfare changes black children in central cities the share living without their parents had more than doubled on average, to 16.1 percent from 7.5 percent, when researchers controlled for other factors.

"What we're seeing is the complex relationship between this thing we call welfare reform and the impact on families," said Wade F. Horn, the Bush administration official who oversees the welfare program. "In some cases we see positive effects on family structures, and in other cases we see more children living in no-parent families."

Mr. Horn said new welfare demands might expose an unfit parent whose children are better off in foster care. On the other hand, he added, a West Virginia mother told to seek work in Ohio may feel obliged to leave a child behind to finish school.

"What it tells us," he said, "is that we need to do an even better job on understanding the complexities of these programs on real people."

In a support group in the Bronx, grandparents raising grandchildren spoke of the many pressures their families faced. Linda Woods, for example, finds it easy to understand how a decline in households with single mothers and a rise in children living apart from both parents could be two sides of a coin.

Ms. Woods's daughter, a sickly high school dropout who once worked in sales, supported her own daughter, China, on welfare after the girl's father abandoned them. Unable to work in exchange for benefits, she eventually qualified for Social Security disability payments and found a boyfriend with a job.

"She got married to him too quick," Ms. Woods recalled. "I tried to tell her, `You're making a big mistake.' " Two years ago, she added, China, then 7, telephoned from her mother's home in Queens, begging to be rescued from conflicts with her stepfather.

Now Ms. Woods, 53 and retired because of ill health, is struggling to care for China without any public aid. China's mother, with a second child to support, has separated from her husband.

Last year, analysts at the nonpartisan Urban Institute reported that the share of children in the United States living in households without their parents rose to 3.5 percent, or 2.3 million children, in 1999, from nearly 3.1 percent, or 1.8 million children, in 1997, a significant increase.

Recently Greg Acs, an author of an upbeat Urban Institute report last year on the rise in two-adult households, titled "Honey, I'm Home," took a second look at his study's unreported results and found that among low-income children, a population more likely to be affected by welfare changes, the share living with neither parent had risen to 5.7 percent in 1999, from 4.7 percent in 1997, double the overall increase.

"If the first story is the decline in kids in single-parent households, then the next story is, where are they going?" Mr. Acs said.

Many, if not most, he said, are living with two parents or a mother and boyfriend. But, he added, "vulnerable children in vulnerable families are increasingly likely to be in no-parent households."

The author of another report on the increase in children in two-adult families, Wendell Primus, now says he has a more nuanced view of his findings. His optimistic take had been particularly influential because he resigned in 1996 as deputy assistant secretary of Health and Human Services to protest what he feared would be the severe impact of the welfare overhaul on children.

"An individual child is sometimes better off living with grandmother, but as a societal matter, more kids living with neither parent can't be viewed as a good thing," Mr. Primus said.

Children who do not live with their parents do significantly worse on average than those in single-parent homes, child welfare experts say, with higher rates of school failure, mental health problems and delinquency.

Some researchers, however, are not persuaded that the upturn in such children is tied to welfare changes. The share of children living without their own parents has fluctuated in the past, with peaks linked to the crack epidemic, AIDS and recessions.

But the economists at the University of California and the Rand Corporation who analyzed the impact of welfare changes on children's living arrangements found a very strong link. Comparing Census Bureau surveys before and after different welfare changes in all 50 states throughout the 1990's, and controlling for other economic factors, they found that on average the share of black children living in cities without their parents more than doubled after the changes even as the share with an unmarried mother dropped to an average of 51 percent from 64 percent.

The effects, researchers calculated, translate into about 200,000 more black, urban children living without a parent.

In contrast, weaker results for Hispanics more consistently fulfilled the intentions of legislators, said Hilary Hoynes, an economist and an author of the study: Hispanic mothers were more likely to be married after welfare changes, and Hispanic children somewhat less likely to live in a single-parent home but no more likely to live without their own parents.

Other researchers suggested that the contrast could partly reflect changing Hispanic immigration, higher marriage and fertility rates by recent immigrants and different cultural traditions in coping with adversity.

One lesson emerging from other recent research, said Doug Besharov, a scholar at the conservative American Enterprise Institute, is that cumulative figures can mask very different, even contradictory effects for different groups and hide the impact of rules that vary from county to county.

"It's an incomplete puzzle," Mr. Besharov said.

The life stories shared in the Bronx grandparents' group help resolve some of the seeming contradictions.

Margaret King, 64, a retired telephone worker with custody of two of her five grandchildren, said that when her daughter lost welfare benefits, the young woman had to depend more on her children's mentally ill, drug-abusing father.

At one point, Ms. King said, after the family was evicted from their Queens apartment and placed in a temporary shelter in the Bronx, the mother became desperate to keep her welfare-to-work job at the city's Human Resources Administration in Lower Manhattan. She left three children with their father at the shelter for lack of a baby sitter, and the youngest, a brain-damaged toddler, cut himself badly on an open can while the father was sleeping off a drinking binge. The mother, who has already turned over her two older children to their grandmother, was charged with neglect and is now at risk of losing the others to foster care.

"She was always a good mother," the grandmother said. "She had no choice, and the system didn't help her."

The King family's experience was echoed in a report last month by Mathematica Policy Research Inc., a nonpartisan research organization. Its study of Iowa's stringent welfare-to-work program found that 7.2 percent of applicants randomly assigned to the program in March 1997 had a child in foster care two years later, compared with only 3.2 percent among those randomly assigned to a control group under the old welfare rules.

Robert Lerman, a researcher at the Urban Institute known for his work on the benefits of marriage, said there was no consensus on the effects of welfare changes on family structure. He was disappointed recently himself, he said, when he sought confirmation of Mr. Primus's earlier finding that the share of black children living with married parents had jumped to 38.9 percent in 2000 from 34.8 percent in 1995.

Looking at newly formed black families in the Urban Institute's large, nationally representative sample, Mr. Lerman instead found a drop in the share of children under a year old living with married parents, to only 26 percent in 1999, from an already low 36 percent in 1997.

Over all, Census Bureau surveys indicate that the number of people in female-headed households declined to 27.4 million in 2000, from 29.2 million in 1995, Mr. Primus said.

But, he added, the number mainly seems to reflect "doubling up and coupling up out of economic necessity, the way poor people have historically managed," a pattern that includes leaving children with relatives.

"The number is still truly astonishing," he said, "but I think the implications of this number are not as rosy as just the number would seem."