The family fled on Wednesday from an investigation home in the Highlands.
They were placed there because they were not judged to be able to take care of the children.
The 15-month-old twins are severely malnourished and must be tube-fed to survive.
At the moment, they weighed about seven kilos each when they should weigh twelve kilos.
Even though the children could not do without tube feeding, the family fled and without taking the tube feeding equipment with them.
The children risk not surviving the journey.
Arrested and wanted
Eksjö District Court decided this weekend to detain the man and woman in their absence, suspected of causing danger to another.
The detention decision states that the parents, through gross negligence, exposed their daughters to danger to life or danger of serious bodily injury or serious illness.
According to the protocol, the parents lack empathy and a feeling for how the children should be taken care of.
The parents are also internationally wanted.