A DIFFICULT question plagues museum collectors today. Who should own works of art that were removed from their original cultures during turbulent historical periods?

The Harvard Peabody Museum has answered that the "original" owners of the works deserve to have them back--at least in some cases. The museum recently returned to the Omaha Native Americans of Nebraska a collection of sacred objects that it had "held in trust for nearly 100 years."

While the musuem should be lauded for deciding to return these artifacts, the phrase "held in trust"--which appeared in the September 21 issue of the Harvard Gazette--reflects the persistent and troubling assumption that museums and collectors have certain inalienable rights to the works of art they hold. This assumption is particularly pervasive in the cases of art from non-Western cultures acquired during turbulent eras.

The case of the Omaha collection is not an isolated one. Museums around the world hold many other art objects "in trust."

But possession alone does not justify the retention of all these works. Museums at Harvard and elsewhere need to consider returning art pieces to the cultures that created them.

Two decades ago, the United Nations established artifact export guidelines that satisfied the international community. Under these guidelines, museums have no legal obligation to consider the conditions under which their collections were obtained, provided the artifacts were acquired before 1970.

But museums still have a moral obligation to do so.

The policies of England, the United States and other world powers during the imperialist era often produced the economic and political turmoil in non-Western cultures that devalued their art. As a result, Western collectors could buy art object cheaply, or simply take them. At the same time, these collectors could argue that they were performing a moral service by "preserving" art from destruction.

The Omaha artifacts were acquired between 1884 and 1889 by anthropologist Alice Fletcher, who later donated them to the Peabody Museum. The collection consisted of animal skins, bottles, shells, and boxes associated with bison hunt rituals and the Sacred Pole, a revered totem that according to the Gazette "embodied the spirit of the tribe." When Fletcher was in Nebraska, the "ritual objects were no longer being used" and would probably have been destroyed had she not saved them.

The objects fell into disuse and were in danger of destruction only because white settlers had progressively wiped out the Native American population over the last century. As Omaha culture was destroyed, the artifacts were no longer valued. They were, therefore, easy prey for eager anthropologists.

Harvard's preservation of the ritual objects for study and exhibition has benefited scholars and museum visitors alike for more than one hundred years. Yet Harvard's decision to return the collection, which occurred in response to Omaha pressure, is a progressive step. It shows the University's sensitivity to the Omaha descendents and their attempt to piece together the fragments of their shattered culture.

THE Omaha request occurred amid a fervent international debate about the ethics of art repatriation. At the forefront of this debate is the dispute between the British Museum and the Greek government over the Athenian friezes from the Parthenon now exhibited in England.

The "Elgin marbles," acquired by Lord Elgin during a period of political turmoil in Greece, might have been destroyed had the British not preserved them. The British also argue that more people can see the friezes in London than would be able to in Athens.

But, the Greeks argue, what good are freizes with fish and chips? Thousands of Greeks cannot see the friezes in their home country. And Greek tourists don't often get to England. More important, the friezes are considered the "crown jewels" of fifth-century Athenian sculpture, and the Greek government strongly desires their return.

Harvard's collection of Tun-huang wall paintings and sculptures in the Sackler Museum should also be considered an important case in the repatriation debate. The pieces were taken from Buddhist cave temples in northern China by Harvard archeologist Langdon Warner in a 1920 expedition. The ancient caves, now preserved by the Chinese government, are marred by gaping holes in the walls where the wall paintings and sculptures used to be.