Laden and Laleh - a 50-50 chance
An international medical team will now begin the most delicate stage of the operation when an attempt is made to separate the brains of the Iranian sisters.
"The next 12-24 hours will be a very critical period," said Dr Prem Kumar, a spokesman for Raffles Hospital in Singapore.
After cutting through the twins' skulls, the doctors have now completed the grafting of a transplanted vein into one of the sister's brains to replace a shared one.
Doctors quietly confident
A team of 28 doctors and 100 medical assistants are involved in the surgery of 29-year-old sisters Ladan and Laleh Bijani, which is expected to continue through the night and most of Tuesday.
The next phase of the surgery - to ensure blood can be drained from both brains - began early on Monday, the statement said.
Iranian President Khatami said the entire
country is praying for the twins
The Raffles Hospital spokesman said the doctors were in good spirits, 24 hours into the operation.
"I can tell you the atmosphere in the operating theatre is very calm, not at all tense because things are very much going according to what the surgeons anticipated. We are cuationusly optimistic," said Prem Kumar.
After the separation the doctors will do the final surgical reconstruction of the skin and soft tissue on the exposed area of their heads, using muscle and skin grafts.
The twins have been told they have a 50-50 chance of survival but say they are willing to risk death for the chance to lead separate lives.
The operation marks the first time surgeons have tried to separate adult Siamese twins - since the operation was first successfully performed in 1952.
German doctors had turned away the Bijanis in 1996, deeming the operation too risky.
Chief surgeon at Raffles, Dr Keith Goh, said he had weighed up quality of life against risk before he could proceed. Both twins are law graduates.
The petite Iranian sisters, who have separately functioning brains encased in one skull, said they knew about the risks, but were still keen to go ahead with an operation they have wanted for years.