JIAGU, CHINA -- When Lin Fengyin found out she was pregnant with her third child, she hid at home to avoid discovery by the village's family-planning cadres. She knew they would press her to have an abortion.

She and her husband had special reason to be afraid. They already had been fined once for violating China's one-couple one-child policy when their second child was born.

When officials in this village in central China's Henan province finally did find out about her third pregnancy, they were adamant about an abortion. Lin and her husband refused. After two daughters, they desperately wanted a son to work the land and carry on the family name. Their wish was especially strong because her husband, Li Baolan, was an only son.

"They came every day for about a month," Lin recalled. By then, she was nearly seven months pregnant. "I was already so big. I could not bear the thought of aborting. So we stood our ground," she said. Two months later, their son was born.

What was wonderful news for the couple, however, was another failure for China's family-planning authorities.

In late 1979, Chinese authorities mandated that married couples have only one child. But as peasant incomes rose and local government control over individuals decreased during the past dozen years of economic reforms, the country's population police realized how difficult it was to enforce an unpopular policy in rural areas where the traditional desire for a male child dates back centuries.

In 1984, the policy was officially relaxed in the countryside to allow those peasants with first-born girls to have a second child after four years.

In recent years, however, because of lax enforcement in many areas, the ability of newly prosperous peasants to pay fines for unauthorized births and an increase in the number of women of child-bearing age, the country's population growth has surged out of control.

In its decade-long struggle to modernize its economy, China has assumed that it will be able to restrict the birth rate. Its failure to do so raises serious implications for improving the economy and living standards, a task seen as more urgent following last year's political turmoil in China.

The latest census results show China's population to be more than 1.13 billion -- about 20 million people more than the goal set by the government for the end of this decade. What is more, the outlook for the future remains grim. The next five years will coincide with a peak of the high-fertility period, officials say.

"My analysis shows that the family planning work in the 1990s will still be arduous," said Peng Peiyun, director of State Family Planning Commission, during a recent press conference. Peng said the commission will increase grass-roots efforts to limit population growth and concentrate on rural areas, particularly in the provinces where birth rates are among the highest in the country, such as Anhui, Henan and Hubei in central China.

In Henan province, for example, the birth rate is more than double that of China's largest city, Shanghai. With 85.5 million people, 84 percent of them peasants, Henan is the second most populous province in the country after Sichuan. The problem is becoming more acute.

"The adverse development of population on the economy has become a shocking fact," Henan's party secretary Hou Zongbin recently was quoted as saying.

In July, the province issued new regulations governing family-planning policies starting at the village level. The new rules call for increased supervision of women of child-bearing age, stiffer penalties for illegal births and strict enforcement of penalties. Each locality sets its own penalties for illegal births.

In addition, family planning will become one of the criteria used to measure performance of all work units, down to the village level, said Zhang Liuran, deputy director of the province's family-planning commission. China's ubiquitous Communist Party-controlled work units regulate the assignment of housing, employment and schooling and are responsible for monitoring the actions of each member.

In the past, party and government officials tended to overlook a work unit's poor family planning record if, for example, it showed good results in boosting output, he said.

But now, he added, a unit's family planning record will be the critical determining factor in measuring performance.

The province is also drafting new regulations to control the province's growing floating population, those peasants who have moved illegally from the countryside to the cities for work. The group mostly is made up of single men or married men who leave their families behind, but it also includes women who want more than one or two children and are trying to escape detection.

Although officials say they do not know how many of the province's unplanned children have come from this sector of the population, currently estimated at about 1 million, they acknowledge that this group is a major source of unauthorized births.

Under the tightened regulations, those who leave their homes must first have family planning certificates listing the number of their children and what type of birth control they use. Once they arrive in a new place, they must present the certificates to the local neighborhood committee and to their employer, who is then responsible for supervising family planning.

Officials acknowledged, however, that such supervision will be difficult and would need much coordination among various government agencies.

Here in Jiagu village, about 65 miles northeast of Henan province's capital, Zhengzhou, party branch secretary Lin Xueshan acknowledged that the family-planning policy has not been actively implemented in the past. Of the 600 households in the village, 130 have at least three children, he said.

Pregnant women often have escaped village pregnancy examinations by living elsewhere with relatives until their babies were born. Inspections of women of child-bearing age have been loosely enforced.

"To tell the truth, we haven't done as well as we should have," he said. "Even when we went to the families' houses to ask where these women went, they refused to tell us their whereabouts."

Since last year, the village has increased its penalties for illegal births from $72 for the second child to $192. The fines are to be levied every year until the child is seven years old. For the third child, the fine has nearly quadrupled, from about $100 -- an amount equal to the average yearly per capita income -- to $385, he said. That fine is to be levied until the child is 14 years old.

Unlike past practice, when the penalty was imposed after the birth of the child, under the new regulations, the penalty is imposed from the start of the pregnancy, he said.

But for couples such as Lin Fengyin and Li Baolan, the penalties no longer serve as a strong deterrent. In addition to their income from planting wheat and corn, Li also owns a small tractor and is able to earn extra money from hauling. The family's yearly income averages $1,100.

They agree that the country's family-planning policy is correct and that they should have been penalized for violating the regulations. But they also said no amount of punishment or penalty was going to change their minds.

"We would have felt differently if we had a boy {earlier}," said Liu, as she nursed her 17-month-old son, Liangliang. "But we felt very, very sad that we did not have a son. We just really wanted a son."