Teen-agers in much of the world are too fat, eat a fatty diet and have high blood cholesterol, smoke too much and even have early signs of high blood pressure, a new study of 5,300 13-year-olds in 15 countries has shown.

All these conditions or habits increase the chances of heart disease, high blood pressure, strokes or some cancers, often early in life.

But American teen-agers arent's generally the worst in any of these categories, except that they are among the fattest.

The finds in 13-years-olds are part of a larger, continuing study of 17,000 boys and girls aged 10 to 15 in the United States, eight European nations (France, Germany, the Netherlands, Greece, Italy, Yugoslavia, Norway and Finland), Japan, Thailand, Taiwan, Kenya, Nigeria and Kuwait.

Among 13-year-olds, the heaviest daily smokers -- "daily" meaning at least one cigaette a day -- were Kuwaiti boys (13 percent) and Yugoslav girls (10 percent). French boys (38 percent) and German and French girls (30 percent) were the heaviest occasional smokers (smoking less than daily).

The findings show "an acute need everyplace for health education in the schools," places where there is little today, said Dr. Errnst Wynder, president of the American Health Foundation, the study's organizer.

The study seems to show that modern, fatty, more westernized diets are having a dire effect in countries such as Japan that once had simpler diets. "Tokyo children," Wynder said, "Now have cholesterol levels as high as American children's." High levels of cholesterol in the blood are an established "risk factor," in medical language, for early heart attacks.

But American 13-year-olds actually had lower cholesterol measurements than those in several nations -- the highest, in order, being Finland, Norway, Kuwait, West Germany, Netherlands and Yugoslavia.

"I think American cholesterol levels, though still too high, are better because there have been changes in our diet," said Wynder, "with people consuming milk with lower fat content and other foods with less fat and cholesterol.

"I also think some teen-agers elsehwere smoke more because those countries haven't had all the anti-smoking education we've had."

As a young chest surgeon, Wynder was one of the first doctors to point to the connection between smoking and lung cancer. The new study's main finding, he said, may be that young people's risk of future disease "depends more on social and nutritional habits than on genetics" or heredity.

Everywhere, he added, the family is less important and children get less home training. Hence the need for health education in the schools.

In many of the 15 countries, the American Health Foundation and other groups are getting government help to start experimental "Know Your Body" program in schools, "We want to make kids aware of the risk factors when they first enter school, then remind them in every grade," Wynder said.

Among detailed findings about 13-year-olds:

Greek, Yugoslav and American boys and Yugoslav, Greek, American and German girls were the heaviest. But by height-weight ratios, a more accurate measure of fatness, Greek, Italian and American boys and Italian girls were the fattest.

The Finnish, French, Greek, Japanese and Dutch and the highest blood pressures, with systolic (or heart contraction) pressures ranging from 112 to 117. There is "some consensus" today, said the study summary, that "optimal" systolic blood pressure at age 13 should be more like 100.

The Finns also had the highest blood cholesterol levels, followed by the other northern Europeans, the Norwegians, Germans and Dutch. All eat fat diets, but the Finns are notorious fat eaters. In Finland and Norway more than half the boys and girls had cholesterol values above 180. The Americans' average was 150. The ideal level for ages 10 to 14 would be 120, though 140 might be a more attainable goal, the summary said.

Among 13-year-olds "daily" smokers: American girls (5.5 percent) and boys (2.7), German girls (5.7 percent) and bots (3.7), and Yugoslav girls (10 percent). Among "occasional" smokers: American girls (19.4 percent) and boys (15.9), French boys (38) and girls (28), German boys (27.5) and girls (30.9) and Yugoslav boys (30) and girls (4.8 percent).