Alfred Nzo came to town this week, inevitably raising the tricky matter of the communist and Soviet ties of the African National Congress, the underground organization that leads the opposition to the white regime in South Africa.

Nzo, a soft-spoken man of 60 based in Zambia, is the ANC's secretary general. He tells people he is a member of the South African Communist Party, which is heavily represented in the ANC national executive council. He bore greetings, in the style familiar to the faithful, to the Soviet communist party congress last March.

Especially at this dramatic moment, it is considered suspect in some quarters -- evidence of hostility to black aspirations -- even to raise this point. It is customarily left to right-wingers, who are then written off for being predictably right-wing. Nzo tightened up when we asked about the communist connection, acknowledged it while trying to play it down, and let an aide parry by suggesting that the Reagan administration pins a communist label on any political elements that don't go along with its "whims."

Some high administration officials certainly do react to the ANC's communist connections, which they see as putting it just where Pretoria's own hard-liners put it: beyond the pale. But, in an argument that goes on, others in the administration have tried to widen the political space open to Pretoria's moderates; they see the ANC communists as one element, and not a monolithic or totally Moscow-driven one, in the ANC coalition, and not as an element that bars American approaches to the ANC's democrats and nationalists.

The administration urges South Africa to free ANC leader Nelson Mandela and accept the ANC as a political interlocutor. Its own internal divisions, however, have kept it from moving its regular quiet talks with the ANC to the policy-making level. Right-wingers howled when the State Department's Chester Crocker cautiously allowed that the ANC qualified ''in a generic sense'' as a group of freedom fighters. Nzo, no stranger to the American bureaucracy, made some sort of garbled bid for an official appointment this week, but no one rushed to receive him.

Part of the administration is being reflexively anticommunist in respect to the ANC, but a serious problem remains. It is the Soviet way to try to capture popular revolutions on a broad platform of justice and nationalism, leaving issues of postrevolutionary organization and orientation to the fine print. The most recent example, a painful one, is Nicaragua.

In the South African case, the Soviet pattern of conspiracy, revolution and centralization of power doubtless appeals to some opponents of apartheid, and Soviet aid of various sorts, including military, appeals to others. To someone enduring the evils of apartheid who knows little of the evils of communism, the former cannot fail to seem incomparably more urgent. Even to someone who knows much of communism, it can seem right and necessary to take aid and comfort from wherever they come. Such a person will naturally resent warnings that he is climbing onto a tiger or contributing to a potentially fateful shift in the global balance of power.

This is what I thought, anyway, reading in Nzo's Moscow speech that the ANC intends to build a "united democratic state" and hearing him suggest that it's really not all that important whether South Africans build socialism on the Soviet model or the Swedish model. Such waffling tends to produce in conservatives a scarcely concealed resistance to the ANC cause and in liberals a measure of hesitation, a choke on full commitment. It can come across to partisans as unforgivably condescending and reactionary and as playing directly into Pretoria's hands. Yet I think that the heart and the head have to be brought somehow into phase.

Knowledgeable people debate whether communist influence in the ANC could survive an ANC ascent to power. Whatever chance there is, however, plainly arises from the inflexibility of South Africa. By holding off on negotiations with representative blacks, it encourages the polarization, violence and chaos on which communism feeds. There can be, must be, intense discussion among Americans and other outsiders over how best to promote negotiations -- by a full-court press on Pretoria, by leaving open a channel of official communication, or whatever. But the focus on a more rather than less peaceful route must be sustained.

This is the overwhelming reason why the United States should get serious about dealing with the ANC itself: to learn its ways, to influence its debates and to draw it away from indiscriminate terrorism and subservience to Moscow toward a dialogue for peace.