Atul Gupta and Duduzane Zuma.

Johannesburg - South African advisory firm Trillian on Friday denied it was paid for work it did not do for state-power company Eskom, saying that it provided various support functions.

The firm, which is being investigated over allegations of corruption, is owned by the Gupta brothers, businessmen with close ties to South African President Jacob Zuma including having previously employed his son, Duduzane.

The brothers have been accused by members of the ruling African National Congress (ANC) of using their political connections to win government contracts. They, and Zuma, have denied any wrongdoing.

A June 29 investigation carried out by attorney Geoff Budlender, which was commissioned by Trillian Chairman Tokyo Sexwale, found that Trillian had been paid 495 million rand ($39 million) by Eskom despite carrying out no work.

Trillian denied the findings and said it was paid for providing technical expertise as well as back office support.

"Trillian maintains that work was conducted for the invoices raised," the company said in a statement. "Trillian therefore wishes to reiterate that it has only billed for work that it had completed and was entitled to."

Eskom and global consultancy McKinsey have opened separate investigations after both companies denied having a contract with Trillian despite working with the firm.

Eskom, which previously said it never paid Trillian, said this week it did pay the firm but as a sub-contractor of McKinsey and at the consultancy's request.

McKinsey says it never had a contractual relationship with Trillian although it did work alongside the firm. McKinsey says a letter written by one of its partners to Eskom asking it to pay Trillian as a subcontractor was inaccurate.

Eskom has paid McKinsey 900 million rand ($70 million) for consultancy work but both parties have suspended their relationship.

McKinsey is one of several companies to be dragged into a scandal in South Africa involving government contracts granted to companies controlled by members of the Gupta family.

Members of the ANC have called for Zuma to stand down over the allegations and a judicial inquiry to be opened.