CUBA AND VIETNAM represent the unfinished business of American anti-communism. They are the two leading countries in which the United States chose to demonstrate its will to combat Communist ideology and/or imperialism. They became symbols of the sort of nationalism the United States could not put down. They remain the only two countries with which Washington does not try to regulate its relations within a framework of mutual recognition.

President Carter evidently intends to tackle these two bits of unfinished business. He's wise to try. There may not be great political or economic gains to be reaped from normalization would let us get on with other things. Progressively fewer Americans seem to find either the improvement of relations with the pair, or the maintenance of the status quo, a moral or strategic imperative. This relative calmness or fatigue - whatever it is - gives Mr. Carter the license he is starting to use now.

Fidel Castro obviously has a finger to the wind. He is cultivating American opinion, playing on the guilt many Americans fell for the assasination plots and the harassment of his regime, and evidently hoping thereby to lower the cost of what he'll have to pay for the credits, security and acceptance he seeks. (He told The Post's Ben Bradlee that the return for our lifting of the trade embargo would be . . . goodwill!) Mr. Carter is asking Cuba to reduce its support to friends in Africa and the Americas, and to free some political prisoners. The immediate interest of both countries in limiting unofficial violence (of hijackers and Cuban exiles) and in disentangling overlapping fishing zones permits a prompt start on what surely will be a long journey back to normal ties.

Vietnam lacks Mr. Castro's public relations genius but it has someting of value - MIA information - to bargain for access to the international economic and political bodies of which Washington is a principal gatekeeper. Hanoi also wants the oil-drilling data the oil companies took home with them. The issues between Washington and Hanoi are not at all that tough. The Ford administration and the House Select Committee on MIAs paved the way for the commission that Mr. Carter is sending to Vietnam shortly to discuss MIAs and take political soundings. Hanoi is ready to make a certain gesture on MIAs. Surely Washington can reciprocate.

So much American emotion has been invested in Cuba and Vietnam that normalization can't proceed simply on some cool calculation of the national interest. Yet it is in the national interest to let past furies subside and to move by stages to the point where we can smooth )to maintain) our differences with these countries in ways commensurate with our stake in international stability and civility. That is what we take Mr. Carter's approach to be.