About 2,000 fewer American babies a year are dying of sudden infant death syndrome since doctors began telling parents to put babies to sleep on their backs instead of their stomachs.

Dr. Eric Gibson of Jefferson Medical College in Philadelphia said this week that the rate of sudden infant death syndrome, or SIDS, had dropped by more than 30 percent in United States.But he said that even more American children could be saved if all parents understood the importance of sleep position.

"Putting infants to sleep on their stomach is an important risk for sudden infant death syndrome," Gibson said at a meeting of the Society for Pediatric Research.

Babies sleeping on their stomachs are more apt to be suffocated by bed clothing. Also, Gibson said an infant sleeping with its mouth and nose against covers can rebreathe exhaled air and become poisoned with carbon dioxide.

In most SIDS cases, babies are found in their cribs not breathing. Many are never revived.

The American Academy of Pediatrics in 1992 recommended that parents put babies to sleep on their backs or sides and in 1994, the National Institutes of Health started a "Back to Sleep" campaign to emphasize the sleep position.

Gibson said that a survey of 3 million births a year since 1989 shows that the U.S. rate for SIDS has dropped from 1.4 per 1,000 babies to about 0.9 per 1,000.

"The deaths have gone from about 7,000 a year to less than 5,000 a year at the end of 1995," he said.

But Gibson said the country could do better. He said a study shows that about 75 percent of white parents now put their babies to sleep on the back or side. Among blacks, there is a 58 percent to 60 percent compliance with the new sleep position.

Among whites, the SIDS rate has dropped by 36 percent, while it has dropped only 16 percent among blacks.

In Australia, New Zealand and the United Kingdom, where researchers first discovered the relationship of sleep position and infant death, the rate of SIDS has dropped by more than 50 percent. Gibson said that studies show about 95 percent of parents in those countries now put infants to sleep on their backs or sides.