IMAGINE THAT the American Civil War has just ended and, as a conscious act of reconciliation, the armies of the two sides are to be joined. What could have been a more impossible task? It didn't happen that way, of course, but something ananlogous is now being tried in Zimbabwe. As a conscious act of reconciliation among factions that had fought bitterly for years, the armed forces are being integrated. That invovles two black armies, one formerly led by Robert Mugabe, now the elected prime minister, and the other by Joshua Nkomo, his political rival, and a third white-led army. It is a measure of the political realities in Zimbabwe that the hard part is to combine the two black armies. They represent different tribes and political tendencies. Mr. Nkomo's actions convey a suspicion that the attempt to integrate forces is calculated to disarm and deny him the option of challenging Mr. Mugabe.

Mr. Mugabe, who has a lot of other things to worry about, has been doing his best to unify the forces, a task made harder by the simulatneous need to reduce their number from a war-swollen 60,000-plus to the 10,000 level.This effort has been imperiled, however, by the resignation -- in frustration -- of Lt. Gen. Peter Walls, the white former foe whom Mr. Mugabe, in a breathtaking gesture of reconciliation, had named as his own military chief. No other Zimbabwean military figure, it seems, has the required personal stature and administrative talent.

It is a critical test for Zimbabwe. The current uncertainty and unrest could degenerate into civil war. Meanwhile, the tension keeps reconstruction from proceeding effectively and scares off the privat capital that is central to the land- and mineral-rich country's development plans.

Enter, maybe, the British. Britain's diplomacy facilitated the transition from war to shaky peace last January. Mr. Mugabe, putting practical needs ahead of hangups and pride, pleaded for high British officials to stay on. But the British sharply reduced their presence on the ground all the same. Now mr. Mugabe desperately wants British help -- ranking, professional, politically neutral -- to help oversee the military transition. The British, who are helping in other ways, seem reluctant to get involved.

But the British have a special responsibility in their former colony -- a responsibility they do not have in some of the other places, like the Middle East, where they are dabbling these days. And they have a special contribution to make arising from their expertise, from the respect still afforded their Sandhurst tradition and from the confidence that their acceptance of the mission would impart. They should do it.