TO biologists, the Galapagos Islands are very special places, not least because their distinctive wildlife prompted Darwin to hit upon the theory of evolution. But the islands, off the coast of Ecuador, have long posed a troublesome evolutionary mystery: geologically, they are far too young for evolution, operating at its usual pace, to have produced the many unique life forms that now inhabit the islands.

A team of oceanographers and geologists has now happily resolved the mystery. They have found evidence that the first plants and animals to colonize the Galapagos chain probably landed on ancient islands that are no longer visible because they long ago sank beneath the waves. Their inhabitants were presumably forced to move on to the younger islands that exist today.

The discovery confirms a controversial hypothesis by two molecular biologists, Dr. Vincent M. Sarich and Dr. Jeffrey S. Wiles of the University of California at Berkeley. In 1983 they predicted that such "drowned" islands would be found. They reasoned that only the existence of long-vanished islands could account for the extensive evolutionary changes undergone by Galapagos species in the period since their ancestors arrived on the islands, which were originally lifeless. Plants and animals are believed to have arrived on the Galapagos aboard seaweed mats or driftwood rafts from the South American continent.

In the current issue of the British journal Nature, a team of researchers say they have found clear evidence that the oldest Galapagos Islands simply crumbled beneath the waves, a conclusion that strongly supports the Sarich-Wiles hypothesis. The authors of the report are Dr. David M. Christie of Oregon State University and his colleagues at the Universities of Oregon and California, Cornell University and the National Oceanic and Atmospheric Administration.

In a 26-day expedition, the scientists made detailed soundings and dredged samples from undersea mountains along the Carnegie Ridge, a submerged crest extending along the Pacific Ocean floor east of the Galapagos toward the coast of South America.

"All along this ridge, and especially around the seamounts protruding from it, we dredged up round basalt pebbles and cobbles," Dr. Christie said in an interview. "We know of no geological process other than beach erosion and near-surface wave action that could produce these rounded forms. The debris that settles to the ocean floor from underwater volcanoes is very different from these. We therefore conclude that these seamounts at one time reached above the surface as volcanic islands, and were later eroded away."

The submerged seamount of the Galapagos chain lying closest to the present-day coastline of South America is about 370 miles west of Ecuador. something less than half the distance from Ecuador to the existing Galapagos Islands. The age of this seamount, whose summit is now some 6,500 feet below the surface of the waves, is about nine million years, the scientists determined. That age is much greater than the estimated two million to three million years of today's Galapagos Islands. Evolution's Chemical Tracks

The existence of an island chain for nine million years would be long enough to account for the state of evolution of the Galapagos animals seen today, biologists say. Moreover, according to Dr. Christie, there are probably still more ancient members of the Galapagos archipelago that remain to be identified, and they may be 90 million years old.

Dr. Sarich and other molecular biologists have demonstrated a chemical basis for the ticking of an evolutionary clock at a more or less constant rate. Essentially, each tick occurs when one amino acid in the backbone chain of a particular protein molecule is switched for another. The protein Dr. Sarich uses for his clock is albumin, and he reckons that in a typical species, between 2.5 and 3 of these substitutions occur in the course of a million years.

He and his colleague, Dr. Allan C. Wilson, now deceased, estimated that because the proteins of chimpanzees and human beings differ by 12 units, the two species must have diverged from their common ancestor about five million years ago.

Dr. Sarich also extensively studied the protein chemistry of several Galapagos species, particularly that of the marine and land iguanas. These two species, Dr. Sarich said in an interview, clearly descended from a common ancestor, a sea-faring pioneer who floated from the South American coast aboard some kind of natural raft all the way to the Galapagos.

Reptiles are able to withstand long periods without water, he said, and this may have made it easier for iguanas to survive immense ocean journeys from South America to the Galapagos, and even to Fiji and Madagascar. But many other species, plants, birds and mammals, as well as the ancestors of the famous Galapagos giant tortoises, must have occasionally survived the ordeal of raft voyages lasting weeks or months from the mainland, carried westward by the Humboldt Current. Having arrived at the islands, they began evolutionary trees of their own that were different from those of their mainland cousins.