RIYADH, Saudi Arabia, April 24— When she was 17, marrying age for a Saudi girl, Salha al-Hefthi was presented with a husband.She was lucky, her parents told her when they planned the wedding, that she was to marry such a good man, a man from her own tribe, a man who would care for their children and make a good living. He was the son of her father's brother -- her first cousin -- and everyone, including the bride, agreed that ''a first cousin was a first choice,'' she said. The couple had two healthy boys, now 22 and 20, but their third child, a girl, was born with spinal muscular atrophy, a crippling and usually fatal disease that was carried in the genes of both parents. Their fourth, sixth and seventh children were also born with the disorder. Spinal muscular atrophy and the gene that causes it, along with several other serious genetic disorders, are common in Saudi Arabia, where women have an average of six children and where in some regions more than half of the marriages are between close relatives. Across the Arab world today an average of 45 percent of married couples are related, according to Dr. Nadia Sakati, a pediatrician and senior consultant for the genetics research center at King Faisal Specialist Hospital in Riyadh. In some parts of Saudi Arabia, particularly in the south, where Mrs. Hefthi was raised, the rate of marriage among blood relatives ranges from 55 to 70 percent, among the highest rates in the world, according to the Saudi government. Widespread inbreeding in Saudi Arabia has produced several genetic disorders, Saudi public health officials said, including the blood diseases of thalassemia, a potentially fatal hemoglobin deficiency, and sickle cell anemia. Spinal muscular atrophy and diabetes are also common, especially in the regions with the longest traditions of marriage between relatives. Dr. Sakati said she had also found links between inbreeding and deafness and muteness. Saudi health authorities, well aware of the enormous social and economic costs of marriage between family members, have quietly debated what to do for decades, since before Mrs. Hefthi was married 23 years ago. Now, for the first time, the government, after starting a nationwide educational campaign to inform related couples who intend to marry of the risk of genetic disease, is planning to require mandatory blood tests before marriage and premarital counseling. Mrs. Hefthi, for one, wishes she had been given the opportunity to test for genetic risks. ''If I knew, I would have said no to that marriage,'' Mrs. Hefthi, an elementary school teacher, said the other night, sitting in her living room with three of her sons. ''Why? It's very painful. Why? If you know something is wrong, would you do it?'' Mrs. Hefthi did not know it when her daughter was born, but Ashjan, now 18, would never walk. Her childhood would be filled with terrible colds, sore throats, assorted other illnesses and an obsessive longing to walk and run like her older brothers. ''Why can't I walk,'' she would shout to her mother when she was 6. ''It is God's will,'' her mother would say. ''In paradise you will walk.'' ''In paradise will I have a magic carpet?'' she would ask constantly. ''In paradise will I have a horse with wings?'' Ashjan would never be able to comb her hair or dress or clean herself. Her body would grow only in tiny spurts, her spine curving into the shape of a half-moon. Once she reached adolescence, she would shrivel year by year, and she would most likely die by the time she turned 20. Health officials and genetic researchers here say there is no way to stop inbreeding in this deeply conservative Muslim society, where marrying within the family is a tradition that goes back hundreds of years. Today, when most unions are still arranged by parents, marrying into wealth and influence often means marrying a relative. Social lives are so restricted that it is virtually impossible for men and women to meet one another outside the umbrella of an extended family. Courtships without parental supervision are rare. Among more educated Saudis, marrying relatives has become less common and younger generations have begun to pull away from the practice. But for the vast majority, the tradition is still deeply embedded in Saudi culture. Statistics on the prevalence of genetically based diseases and the extent to which they are a direct result of marriage between close relatives -- second cousins or closer -- are scarce or unreliable because many Saudi parents raise their disabled children in obscurity, ashamed to seek services. That has begun to change as more programs intended to educate disabled children open in Saudi Arabia, where there were almost none until a decade ago. Genetic research is emerging here and several projects have recently begun in an effort to document the connection between inbreeding and disease and to quantify the prevalence of the diseases. ''Saudi Arabia is a living genetics laboratory,'' said the executive director of the Prince Salman Center for Disability Research, Dr. Stephen R. Schroeder, an American geneticist who has been doing research in Saudi Arabia for the last year. ''Here you can look at 10 families to study genetic disorders, where you would need 10,000 families to study disorders in the United States.'' One of the oldest and best known educational programs for disabled children in Saudi Arabia is the Disabled Children's Association in Riyadh, which opened in 1986. There, 200 children from infancy to age 12 suffering from a variety of diseases and disorders attend day care programs and classes. At the school, the director, Sahar F. al-Hashani, pointed out at least one or two students in each of six classrooms whose parents were related. Not all marriages between close relatives produce children with genetic disorders. In fact, most do not. But testing could identify couples who test positive for serious diseases. Under a fatwa issued by the World Islamic League in 1990, Islam permits abortions up to 120 days after conception if an unborn child tests positive for a serious disorder. In the case of spinal muscular atrophy, if both parents are carriers of the gene, the couple has a 25 percent chance of having a child with the disease -- or one in four children. The percentage regrettably turned out to be much higher for Mrs. Hefthi and her husband, with four out of their seven children afflicted. Mrs. Hefthi said she would not allow any of her three healthy boys to marry a relative. In a society that places such a premium on having children, she said, many people would choose to find another mate if they learned that they were at risk of having severely disabled children and if their parents supported their decision. ''I suffered,'' she said. ''People, sometimes when they see me they say how tired I am. They tell me I could put my children in an institution. But I tell them I am a mother.'' Photos: Muhammad al-Hefthi, right, and his brother Ahmed, center, have spinal muscular atrophy. Abdulrahman does not. Of the seven children of their parents, who are first cousins, four were born with the disorder. (Sarah Kershaw/The New York Times); A Saudi poster urges premarital counseling and blood tests.