The first murder was at Mariveni village in Ritavi, said Lt-Col Moatshe Ngoepe.
A 42-year-old man was arrested for killing Winter Mbodi Ntimana, 40, by driving his car into him at high speed, then reversing over him, after an argument.
“The suspect will appear before the Ritavi Magistrate’s Court soon on a charge of murder,” said Ngoepe.
The second murder was at Segwashi village near Haenertzburg.
A 45-year-old was arrested for allegedly killing his 50-year-old girlfriend.
“It is alleged that the suspect killed the deceased and buried her body in a shallow grave until we got information which led to his arrest,” said Ngoepe.
“The motive behind this incident is still unknown, but our investigations will give more light on that.”
The 45-year-old man was expected to appear in court soon.
Both men were arrested on Sunday night.