A medical team of 30 doctors working in shifts toiled for 18 hours Saturday and Sunday to surgically separate twin Iraqi girls who have been joined at the chest and abdomen during their 11 months of life. The operation ended early Sunday for Fatma and Zahra Haidar. "They are stable and they are responding very well to the surgery," said the chief surgeon, Dr. Abdullah Al Rabeeah. "We have to watch them day by day, but we are optimistic." The most critical immediate concern is the risk of infection, he said. The children were flown to the National Guard King Abdul-Aziz Medical City health complex for the operation after Custodian of the Two Holy Mosques King Abdullah Bin Abdulaziz heard a televised message from their parents asking for help. Al Rabeeah said it had taken nine months for the malnourished children to gain enough weight to withstand the operation, which has at least 10 phases. "Their chances for recovery are good," although infection is a concern in the early stages after the surgery, Al Rabeeah said. Each girl will have to be fitted for an artificial leg. The doctors first detached the girls at the chest, abdomen and pelvis, then proceeded to separate shared organs -- the liver, small and large bowel, urethra and bladder and genitals, Al Rabeeah said. "Now we are reconstructing their organs," the surgeon said about 10 p.m. Saturday night (2 p.m. ET). "Each of them will require an artificial leg. ... And after that, their expectation is going to be good. They will have a handicap, but they will overcome that handicap with careful rehabilitation and a physiotherapy program," the surgeon said. After surgery, the girls will spend a week in pediatric intensive care, and remain in the hospital another few months.