The unravelling in recent months of a lavishly financed, secret South African government campaign to influence public opinion abroad has seriously damaged the political standing of Connie Mulder. Once acknowledged as the likely successor to Prime Minister John Vorster.

Mulder, the 52-year-old Minister of Information who is also responible for the ministry dealing with South Africa's black majority, has been tarnished by association with the wrong-doing of two of his former subordinates.

In the wake of the scandal, the section involved is to be completely restructured. The two subordinates - Eschel and Denys Rhoodie - were accused of a host of financial irregularities in a government probe and pensioned off.

Mulder had been regarded as the "crown prince" to Vorster, accordiing to one South African newspaper editor, "but he's at the lowest point of his popularity right now. He'll have to get rid of some of the image he's gotten, some of that stigma . . . to make up now in the prime ministership race."

The secret fund activities intended to improve South Africa's image abroad, were carried out by a department of the Information Ministry. Most details remain cloaked in secrecy.

It is alleged in the South African press that some of the money paid for full-page, pro-South Africa ads in such papers as The Washington Post and The New York Times, taken out by a mysterious "Club of Ten" in London.

There are also reports, thus far unconfirmed, that the funds went to South Africa's only English-language pro-government newspaper, The Citizen.

In its zealousness to promote the South African viewpoint and counter its critics, the department often committed clumsy gaffes and angered those it tried to influence. U.S. congressmen complained recently when agents of the department entered closed meetings without permission.

When anti-apartheid editor Donald Woods addressed a committee hearing, a man linked to the department, Retief Van Rooyen, vociferously challenged Woods' testimony.

So far, Mulder has not been accused of complicity in any of the financial irregularities of the Rhoodie brothers, which involved taking wives on government-paid trips, submitting inflated expense accounts, overpaying publishers for books and making travel arrangements through private travel firms - rather than through government agencies as is government policy.

But in public statements and in testimony before a parliamentary committee, Eschel Rhoodie said Mulder had knowledge of all Rhoodie's activities and at one point, even asked Rhoodie "to keep secret the information that a travel voucher had been falsified to hide the fact that Deneys Rhoodie's wife accompanied him on a government trip abroad. Mulder said later he allowed wives to go along for "humanitarian" reasons.

It has also come to light that Perskor, a publishing firm of which Mulder is a director, received more than $3 million worth of printing jobs from the Department of Information in 1977; and that Mulder, with the Rhoodie brothers and with his close friend, Michigan publisher, John McGoff, formed a company which owns a game farm in northeastern South Africa.

While these activities are not illegal, one Afrikaner pointed out, "they're just not done."

To the rank and file of the National Party, most of whom are struggling middle class people with a strong strain of honesty, these financial dealings are suspect and Mulder, as head of the department, is accountable. Prime Minister John Vorster's quick and decisive moves with the Information Department reflect his concern about his all-white electorate's sensitivity to financial improprieties.

According to one newspaper report, Vorster rebuffed an attempt by Mulder supporters within the party to have the parliamentary inquiry shut off and to allow the department of information to remain under Mulder's ministry.

Comparisons have been made between Vorster's swift action against Mulder and the Rhoodie brothers and the absence of similar moves against Ministry of Justice officials when black consciousness leader Steve Biko died in police custody last September.

Significantly, the comparison was first made by an Afrikaans language newspaper, Rapport, which commented that the Biko case "still leavts a bad taste in the mouth . . . and has made many wonder how it was possible that top heads did not roll in that case, too."

Vorster has always been overly discreet - some say to the detriment of the party - about whom he favors as a successor. Some speculation has suggested he may step down as early as 1979 or 1980. Pik Botha, the 45-year, old minister of foreign affairs, has been regarded as the candidate from the moderatt faction of the party.

From the conservative wing of the party P. W. Botha, the 62-year-old minister of defense, and Mulder have been the contenders.

Mulder is certainly still in the running to inherit Vorster's mantle. To recover, however, he must be eminently successful in his job as head of black affairs - and that may require a whole new direction from Mulder.

It will demand that he take steps which in the South African context are "liveral," making him less popular with his traditional conservative power base but probably gaining him support among the moderates.

"I can't see that this scandal, as you call it, can harm Mulder," said Dennis Roodt, an Afrikaner banker. "Sinct he took over as minister of black affairs, he's made an impact on moderate Afrikaners who want change. Someone who is prepared to talk to the blakes. That is strongly in his favor," Roodt said.