IT WAS A MISSION impossible from the start that the Lancaster House conference -- which laid down a plan to move from war through a cease-fire to majority-rule elections in Rhodesia -- assigned to Lord Soames. He was given near-absolute powers in theory but no effective muscle of his own in fact, and was told in effect to take a set of mirrors down to Salisbury and make the whole fantastic enterprise work.

In almost two months on the job, Lord Soames has labored mightily, applying the same brash no-nonsense tactics by which Britain achieved agreement at the Rhodesia peace conference. He has gotten the four or five separate armed parties to stop most of their shooting (though intimidation remains a pervasive election tactic), and he is on the way to carrying off what are not only the first full free elections in Rhodesia but fuller and freer elections than practically and other peaceful African country has ever known.

Yet as the election period nears, it is evident that the political structure Lord Soames is laboring to poke and cajole into being just might collapse as soon as it is formally put into place. It is not simply that none of the public and private armies has been disbanded and disarmed, although that is a consideration. Nor is it simply the danger that has existed from the beginning that the losers of the election might not accept the verdict -- and that the winners might take their victory as a mandate to finish off the losers.

It is that the run-up to the elections has tended to be reduced to a contest of wills between two very different and very strong-willed men, Lord Soames and Robert Mugabe, the guerrilla leader whose likely capture of a plurality in the elections has provoked a stop-Mugabe movement among his rivals. And while Lord Soames will go back to Britain in two weeks, Mr. Mugabe will stay -- either inside the political process as a politician or, possibly, outside as a guerrilla fighter again.

Lord Soames: a white brahmin of the formerly colonial establishment determined to hand Rhodesia over to majority rule by blacks but feeling a deep Tory obligation to the remaining whites -- two purposes whose subtle but unavoidable disharmonies are particularly audible to African ears. Mr. Mugabe: a black nationalist and revolutionary pressed in one direction by allies in the front-line states eager for peace and pressed in another by followers, some plainly beyond his control, wary of any diplomatic or political process in which whites have a role. These differences have glinted through a series of arguments on specific issues: the presence, since ended, of South African troops to guard what is understood to be the white "escape route" to South Africa; the refusal of perhaps 5,000 or more Mugabe guerrillas to enter the agreed assembly camps; and Lord Soames' threat to disenfranchise voters in districts where Mugabe guerrillas and Mugabe voters are strong.

A lot of Americans and others are apprehensive about the Soames-Mugabe connection but feel that there is no real choice at this point except to acknowledge that it is a British show. Well, it is a British show; but there is no doubting either that, if it were to collapse, the United States would surely be called on to pick up a major share of the pieces. This is as tense and consequential a moment as there has been in the Rhodesian enterprise, and Americans can do little but watch and hope.