AN Adelaide man who admitted killing his partner has now also pleaded guilty to murdering her two children.

Steven Graham Peet killed Adeline Yvette Wilson-Rigney and her children, Amber, 6, and Korey, 5, at a property north of Adelaide in May, 2016. His trial in relation to the children was scheduled to resume on Monday, but Peet entered guilty pleas instead.

The change followed a recent psychiatric report.

The bodies of Ms Wilson-Rigney and the children, aged five and six, were found in a house at Hillier.

All three had cable ties around their necks and their bodies were hidden under clothes and bedding and, in the case of the boy, under a child's play tent. The young girl had adhesive packing tape wrapped around her head and a sock had been stuffed in her mouth.

The boy had parts of his body wrapped in packing tape and his hands and feet were secured behind his back in a hogtied fashion.

Peet initially pleaded not guilty to the murder of the children, claiming he was in a disassociated state at the time.