The ANC, which holds 63 per cent of seats in the national assembly, is "on the verge of a two-thirds majority", according to the Human Sciences Research Council survey of voter intentions for the 2 June poll.
It gives the runner-up New National Party (NNP) 8 per cent of the vote, down from 12 per cent four months ago. The ANC has increased its share from 57 to 62 per cent.
As the 15 parties fighting South Africa's second free elections begin campaigning in earnest this weekend, the only question is how great the ANC's majority will be. It is already known that President Nelson Mandela will retire after the election, handing over on 16 June to the current leader of the ANC, Thabo Mbeki.
Even though the ANC's first experience of government has been far from trouble free - unemployment and crime levels have never been so high - most South Africans are immeasurably better off than they were under the old apartheid regime.
The ANC has presided over schemes which, since 1994, have taken electricity to two million more homes and water to a further three million, given away thousands of acres of land and brought telephones to 1.5 million new households.
Health care and education provision have been a disappointment as resources do not match needs, and a programme to build a million homes has not been completed due, in part, to corruption and mismanagement.
With a murder rate seven times that of the United States and unemployment at about 40 per cent, South Africa might seem fertile ground for strong opposition. But the alternatives to the ANC are still tribally and racially rooted and generally hardline, calling for ultra-liberal economic policies and restoration of the death penalty.
The formerly ruling NNP - renewed essentially only by the addition of an "N" to its acronym - seems headed for extinction outside its Western Cape heartland. Its main challenger for votes from whites (12 per cent of the population) is the Democratic Party, whose supporters are younger and urban but, according to the survey, inhabit mainly the Johannesburg area, whose majority black population is overwhelmingly pro-ANC.
So well does the ANC score in yesterday's poll that Kwa-Zulu-Natal - the fiefdom of the Inkatha Freedom Party (IFP), headed by the home affairs minister, Mangosutu Buthelezi - could be heading for a hung provincial parliament. The ANC leads the IFP by 7 per cent in the area, which includes Durban.
Similarly, for the first time the ANC is a real threat to the NNP in the Western Cape. In an area dominated by "coloured" (mixed-race) voters who feel alienated by the black majority, the ANC in this survey is ahead of the NNP. The Western Cape and KwaZulu-Natal are the two areas where there are the most fears of pre-election violence.
Party support profiles show that the ANC has maintained a solid support base among black people (70 per cent of supporters), while the NNP and the DP have mainly white support (51 and 45 per cent respectively).
Only one new party, the United Democratic Movement (UDM) plays an overtly cross-racial card with its double act leadership of Bantu Holomisa, black and from the Eastern Cape, and Roelf Meyer, a "born-again" National Party cabinet minister. But the UDM's support, in this survey, has declined from 6 to 3 per cent.
In common with other small parties, the UDM has blamed financial constraints. Mr Meyer said: "We find that the corporate supporters want to help the `politically correct' ANC. They do not have a vision of the need for an opposition to guarantee a healthy democracy."
On yesterday's survey, the 15 opposition parties will gain about 19 per cent of the vote - 5 per cent less than in 1994.Reuse content