The doctors at All India Institute of Medical Sciences (AIIMS), New Delhi for the first time attempted to separate twins joined at the head on Monday.
Jaga and Baliya, two years and three months old, born to farmers from Odisha's Kandhamal district, were referred to AIIMS last month.
Doctors say, the operation is more complicated because they share veins that return blood to the heart from the brain.
"We are hoping to save both but even if one of the twins survives, it will be a historic achievement," a doctor said.
Twins joined at the head are very rare, occurring once in 25 million live births. Since 1952, only about 50 attempts have been made to separate such twins across the world.
"This attempt to separate them, if successful, will provide hope and test the frontiers of science," a doctor said
Will Jaga and Baliya be separated for good?
Check out the video to know more.