The most important thing now is to protect the two from infection and ensure they have no breathing difficulty, said Truong Quang Dinh, the hospital's deputy director.
The two babies are suffering increased chest and abdominal pressure after the 12-hour operation. Phi Long is in relatively stable, except for a mild fever and a bit fast heartbeats.
His kidneys do not function properly due to increased intra-abdominal pressure, but this problem can be solved, Dinh said.
Doctors are now keeping a close watch on the health of Phi Phung who is at risk of infection.
Both Long and Phung undergo blood tests every 12 hours to see their biological variation.
About 70 surgeons, anaesthesiologists and nurses took part in the operation on the twins, 14 months old, joined at the abdomen and chest.
