The case was adjourned to October 26 after Duduzane’s lawyers asked for more time to prepare his defence.
Duduzane Zuma on trial
34-year-old Duduzane appeared in court, accompanied by his father, to face two charges over a car crash in 2014 when his Porsche 911 ploughed into a minivan taxi in Johannesburg, killing one woman and injuring another who later died.
State prosecutors initially decided not to charge Duduzane, who denies any wrongdoing.
He has previously said he lost control of his car after it hit a puddle of water.
The National Prosecuting Authority however curiously took up the matter after Jacob Zuma resigned as head of state following a recall by the ruling African National Congress in February.
Indeed, many of Zuma’s supporters have called for the case to be settled out of court, arguing that he is being persecuted because of a witch hunt against his father.
In July, Duduzane appeared in leg irons at another Johannesburg court on corruption charges, which his lawyers say he will contest.
He was released on bail of 100,000 rand (6,800 dollars).
Jacob Zuma on trial
Meanwhile, Duduzane’s 76 year old father is also facing charges of fraud, racketeering and money laundering relating to a $2.5 billion arms deal in the late 1990s.
Jacob, like his son, Duduzane denies wrongdoing.
The charges over the arms deal were previously filed but then set aside by the National Prosecuting Authority shortly before Zuma ran for president in 2009.
After his election, his opponents fought a lengthy legal battle to have the charges reinstated, finally succeeding in 2016.
Also this week, an inquiry into claims of influence-peddling against former South African president Jacob Zuma, started hearing witnesses and receiving testimonies.
The commission is investigating allegations that the Gupta brothers, who headed one of the nation’s largest conglomerates , unduly influenced Zuma over political appointments and winning government contracts.