One explanation, Dr. Babcock said, might be that most trilobites themselves favored their right sides, and that they instinctively veered to the right when trying to escape. Another explanation could be that the predators were predominantly "left-handed," tending to attack the trilobite's right rear. A third possibility is that both predators and prey exhibited preferences in their behavior. From the present evidence, there is no way to tell which of these explanations is correct, Dr. Babcock said in an interview, "but there seems no doubt that handedness was common among the creatures of the Cambrian and post-Cambrian periods."

Dr. Babcock examined more than 300 trilobite fossils, all exhibiting malformations of various kinds. Some of the wound scars were attributable to accidents that might have happened while trilobites were in their soft-shell phase, while they were mating or in some other way. These trilobites were discarded from the survey. But of the animals clearly displaying healed bites, more than 70 percent had been injured on their right sides.

Evidence from well-preserved fossils shows that a trilobite's organs were essentially symmetrical, so there is no apparent physical reason why a predator should find one side of a trilobite particularly tasty.

Scientists cannot be sure which species were the main enemies of trilobites, but the shape and size of many of the bites chewed from trilobite shells match the circular, nutcracker mouth of a primitive animal called Anomalocaris -- a 20-inch-long creature with no known modern descendants. Fossils of Anomalocaris are abundant in the same sediments as those of the trilobites. Possible Role in Survival

Dr. Babcock said he believed that asymmetric behavior helped species to survive, and that handed preferences have probably been common in animals, plants, bacteria and even fungi almost since the dawn of life.

In many cases, handed behavior is related to nonsymmetrical body parts or some asymmetry in the function of an animal's nervous system. The manual preference of right-handed people, for example, is believed to stem from the dominance of the left hemispheres of their brains. Also, the right hands of right-handed people tend to be slightly larger than their left hands, Dr. Babcock said, and some glove manufacturers make right gloves about 4 percent larger than their mates.

Present-day lobsters and other crustaceans generally have one dominant claw, probably because of some asymmetry in their nervous systems. Lobsters can adapt themselves to favoring the other claw, however, if the dominant claw is injured.