Northern Cape ANC leader John Block and two other provincial ANC heavyweights Yolanda Botha and Alvin Botes, and Trifecta director Christo Scholtz, face charges of fraud, corruption, and money laundering.
Northern Cape National Prosecuting Authority (NPA) spokesperson Mashudu Malabi said it was ready to continue with the trial on Monday.
She said all accused except Scholtz were present at court.
Malabi said the defence counsel asked the court for a postponement.
She said the State agreed to the postponement, and that the trial would start on 3 February.
A warrant of arrest for Scholtz was authorised and would be held over until February next year.
The NPA has alleged that the Trifecta Group entered into a number of lease agreements with the Northern Cape social development department in which rentals, or rental space, were grossly inflated.
As a result, the Trifecta Group received, or would receive, rentals of R57m at the end of the lease agreements.
The NPA said earlier the case was part of the on-going work of the Anti-Corruption Task Team set up by Cabinet in July 2010 to deal more effectively with large corruption cases.
On Monday, the DA protested outside the high court.
Northern Cape DA leader Andrew Louw said the further postponement of the matter was unfortunate.