Petros Williams, 37, is charged with killing his son Theo Molemohi, two, and his four-year-old daughter Yolanda.
Their mother Morongoe Molemohi, 30, who was recently estranged from her husband, discovered the unconscious youngsters at a flat in Whalley Road, Whalley Range, Manchester, last Wednesday morning.
They were pronounced dead a short time later. Williams was found collapsed at the scene and was arrested.
A post-mortem examination found the children had been strangled.
Williams appeared before Manchester Magistrates' Court wearing a white T-shirt and blue jeans.
He spoke only to confirm his name, age and address, and to indicate he did not require an interpreter.
Kieran Henry, for the defence, made no application for bail.
Magistrates remanded him into custody and he will appear before Manchester Crown Court for a plea hearing on January 4.