In the almost 20-hour-long surgery, the doctors performed venous bypass to separate the veins shared by the babies that return blood to the heart from the brain.
"The surgery began yesterday at around 9 am and went on till 5 AM today. The children are under observation," a senior doctor at AIIMS said.
According to the doctor, the surgery to separate them will be taken up by October end.
The twins--Jagannath and Balram--from Kandhamal district in Odisha, are craniopagus conjoined twins who are joined at the head. This is a very rare condition.
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A series of investigations, including multiple MRIs, CT scans and angiograms, were carried out on the twins to see to what extent the veins in their brains are fused and whether surgery was feasible.
The twins were shifted to AIIMS on July 13.
Deepak Gupta, professor of neurosurgery, earlier had said the twins suffer from the condition which afflicts one in 30 lakh children, of which 50 per cent die either at birth or within 24 hours.
"Also, there is less than a 20 per cent chance of survival among those who undergo this surgery. Such operations are extremely challenging," Gupta had said.