The battle against illicit drug use, says Attorney General Edwin Meese, "is a marathon, not a sprint." His point is illustrated in two studies released this week, one by the Drug Enforcement Agency and another by University of Michigan's Institute for Social Research. Both reports show some encouraging progress offset by other new or growing problems. In spite of a five- year sustained effort to prosecute traffickers and educate the public about the hazards of abuse, serious problems remain.

The DEA's annual report gives us a picture of drug use and trafficking in the country as a whole. In 1984, marijuana use was down, but cocaine use rose 11 percent in a single year. The frightening practice of injecting this drug in combination with heroin is also on the rise. And, in spite of the fact that clandestine laboratories that manufacture PCP and illegal amphetamines were shut down at a rate of almost one a day, use of these dangerous drugs rose by 15 percent.

The University of Michigan study, also part of an annual series, tracks drug use by high school seniors. Here we learn that an encouraging five-year decline in this area has now stalled. Even marijuana use, which had been cut in half since 1978, remains stable in this age group. Cocaine, tried at some point by 17 percent of the seniors, is now the third most frequently used drug after marijuana and amphetamines. This is true even though a large majority of the youngsters interviewed acknowledge the harmful long-term effects of the drug.

It is also discouraging that the recent decline in the use of legal substances -- alcohol and tobacco -- has ended. Twenty percent of the seniors smoke cigarettes every day; 45 percent of the boys and 28 percent of the girls admitted to heavy drinking (more than five drinks in a row) during the two weeks before the survey was taken.

It is no distinction that the rate of illicit drug use by young people is higher here than anywhere else in the industrialized world. Perhaps this year's figures are a quirk, a small deviation from the trend that will correct itself soon. Nevertheless, the numbers are cause for concern and a renewal of effort by law enforcement officials and educators. A sustained attack on this problem, even where the gains are small and slow, has the support of the public.