IS IDI AMIN, the butcher who has ruled Uganda for eight years, on the way out? Long ago his murders of some hundreds of thousands of Ugandans and his destruction of the fabric of the society had ensured that, when a serious armed challenge to him finally was mounted, he would have only a diminishing circle of mercenaries on whom to rely. That challenge is being mounted now, mainly by the army of neighboring Tanzania, which is in effect counterattacking for President Amin's invasion of Tanzania last fall. Several factions of Ugandan exiles are also said to be in the field. Amin's own troops seem to be both falling back and fading away. Even his erstwhile patrons and arms suppliers in Libya and the Soviet Union are keeping a distance. He has signaled his distress by soliciting African mediation, but no response has been forthcoming.

Tanzania's president, Julius Nyerere, deserves most of the credit for the events developing now. Africa's old-boy net kept the Organization of African Unity from condemning Uganda's attack on Tanzania last year. In many places in Africa, moreover, distaste for Amin's barbarism is muted by admiration of his defiance of the West, especially Britain, the former colonial power. Undeterred by Africa's cop-out, Mr. Nyerere accepted a responsibility to act alone. Hence his army's current drive into Uganda and his support of Ugandan exiles.

Mr. Nyerere insists that his purpose is to safeguard Tanzania's territory and honor and that any change of regime in Kampala is the business of Ugandans themselves. In this manner, he pays homage to the African doctrine of non-intervention. All the same, his policy is making a Ugandan change of regime possivle. Political condemnation and economic reprisal by non-Africans had weakened Amin but failed to drive him to the wall.

The rejoicing, if the Amin regime should fall, will have to yield quickly to the tasks of reconstruction. The country's human capital has been depleted by death, dispersion and neglect, its economic and social plant is a shambles, its new politics could well reflect some of the same unhappy tensions that marked the pre-Amin period. Yet the country's release from the grip of Africa's bloodiest tyrant would be bound to liberate the energies and talents of its people, and they can expect the help of Uganda's friends.