ANYONE FOUND swimming in the Rhine, says the mayor of Dusseldorf, Germany, is considered to be attempting suicide. Though he says this with a smile, it is not a joke. The Rhine is so polluted that a single bottle of its water exhibited at a trade fair last year was found to contain 105 different chemicals. Altogether, the river -- which is the source of drinking water for 20 million Europeans -- is believed to contain 2,000 different chemicals. Many of them, including thousands of tons of chromium, lead, zinc, arsenic and mercury, are toxic. Raw sewage and heated water are also major problems.

Only a few miles from the mouth of the Rhine is the other side of the water pollution story: the Thames. Twenty years ago, the Thames was also an open sewer. Birds, fish and even barnacles had disappeared. When the smell got so bad that it disrupted sessions of Parliament, a serious commitment was made to clean the river up. Many believed that the money would be wasted -- the river seemed beyond redemption. Today, however, the Thames is beautiful. The birds are back by the thousands -- a sure sign of clean water. Shrimp and salmon -- among the pickiest of fish -- have reappeared after an absence of nearly 100 years. And water-skiers -- yes, on the Thames -- have become a hazard to navigation.

Part of the difference lies in the heavier industrial activity along the Rhine, and part is due to the stronger central power of the British government. But most of the difference comes from the fact that the Thames flows through only one country, while the Rhine flows through seven.

Some more good news, however, is that for the first time there is now reason to believe that bodies of water bounded by many countries are not automatically condemned to permanent pollution. While international efforts to clean up the Mediterranean are foundering, a success story is unfolding in the Balitic Sea. There the seven littoral states have signed a binding agreement covering everything from biological monitoring to ship safety. Each country has been assigned chief responsibility for the research and monitoring of a major hazardous pollutant: Denmark for PCBs, the Soviet Union for mercury, West Germany for lead, Poland for DDT, etc. Sweden has come up with a way to "fingerprint" oil so that spills can be traced to the culprit.

In this country many of those concerned with the nation's natural resources are predicting that water problems -- quantity and quality -- will be a central issue of the coming decade, and as difficult as energy has been in this one. So the news from Europe is timely. International complications are not as great a problem here, but with water from the still uncapped Mexican oil well fouling Texas beaches, the Baltic agreement is worth a serious look.