Mario-César Deus Yela, 49, wearing a black hoodie and stukkende jeans, appeared in the Wynberg Magistrates' Court yesterday but did not apply for bail as was expected.
The court said it would first deliver a ruling on whether the defence would be allowed access to the police docket.
His bail application would follow on 28 July.
Post-mortem reports to establish how the children had died are also still outstanding, as well as a toxicology report and cellphone records.
Yela is currently being held in a single cell at Pollsmoor Prison.
He allegedly killed his children Maximo and Octavia at a rented holiday home on 16 April.
His ex-wife found their tiny bodies on the day he was supposed to return to Spain.
The defence is considering whether to refer the accused to Valkenberg Psychiatric Hospital for mental observation. Yela is apparently in a “fragile mental state”.
It was revealed in court that he had apparently sent a message to his ex, Julia Engelhorn, asking her to come over for lunch.
When she arrived, Yela allegedly told her he had killed the twins.
The shocked mom found their bodies in the bedroom. Their older sibling was still at school.
Yela then allegedly threatened to kill Julia with a knife, but she managed to escape.
Yela had allegedly fled the scene in the mom’s car. Police tracked down her car to Wynberg, where Yela was arrested.