He told the court that he will not be applying for bail and opted for legal aid representation.
The case has been postponed to next month for further investigations.
Mpungose was arrested a day after the killings.
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The bodies of 4-year-old Kuhlekonke, 6-year-old Khwezi and 10-year-old
Sphesihle Mpungose were found in their home on Tuesday afternoon by
their distraught mother and the police.
Their older sister, 16-year-old Ayakha Jiyane was found in a bush in New Germany, west of Durban.
She had been on her way to the gym, but says she could not get out of the car while the news report was being read on radio.
"I was shocked, I went to the boot, but couldn't switch off the radio. I was so shocked, I had to get back into the car and listen."
Mpungose is due back in court on the 9th of October.
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