One of the conjoined twins separated at London's Great Ormond Street Hospital has died.
Hope Williams - whose sister Faith is said to have a 50/50 chance of survival - died because her lungs had failed her, Professor Agostino Pierro said.
Laura Williams, 18, from Shrewsbury, gave birth to the girls at another London hospital on 26 November.
The twins, who were joined at the chest and shared a liver but had separate hearts, were separated on Tuesday.
Mrs Williams and her husband Aled, from Anglesey, were with Hope when she died.
Professor Pierro, head of the surgical team which operated on the girls, said Faith still needed support for her breathing.
He said she was in a stable condition and "gradually improving", but warned there may be complications.
HOW THE TWINS WERE JOINED
The twins shared a liver and circulatory system. Hope was the smaller of the two.
A team of 20 led by Professor Agostino Pierro performed an operation lasting 11 hours.
After separation, Hope's lungs failed and she died.
Faith is in a stable condition. More surgery will be needed on her abdomen. She is said to have a 50/50 chance of survival.
The team continued to operate on Faith after Hope's death and the whole procedure took about 11 hours.
Faith will need further surgery to close her stomach and is in intensive care.
The hospital had wanted to wait until the twins were stronger before carrying out the operation, but it was brought forward after their health gave cause for concern.
Professor Pierro said: "This was an emergency operation because there was a blockage in their joined intestine which could only be resolved through separation.
"The technical separation worked well, although it was extremely challenging, and went according to plan."
Jessica Culver, a friend who has a son close in age to the Williams' 18-month-old daughter Carly, spoke to Mrs Williams after Hope died.
"Last night she phoned in tears, a bit upset, saying that Hope hadn't made it but Faith was doing well," she said.
"I think it was relief for Faith but obviously she was devastated for Hope."
Challenging and complex
Ms Culver, who went to school with Mrs Williams, added: "I can't say that I understand because I've never lost a child.
"It was just really difficult. I mean, finding the right words to say to her and just trying to show her that she's still got Carly and she's got Faith as well to look forward to bringing home.
"I know it's not going to be as good as taking home both of them, but at least she still has got Faith left."
Professor Pierro added that he was sorry for Mr and Mrs Williams' loss.
"The parents are coping extremely well and I am grateful to them for their support," he said.
Professor Agostino Pierro: 'The operation was very challenging'
More than 20 staff were involved in the operation and Professor Pierro said it was one of the most challenging and complex he, and hospital staff, had ever faced.
"We separated the babies and unfortunately, after separation of the babies, Hope's lungs were too small to support her breathing and circulation.
"So eventually she died because of a lung condition and in reality what happened before is that the lungs of Faith were somehow supporting Hope," he said.
Staff at Great Ormond Street Hospital are considered to be among the most experienced in Europe in separating conjoined twins.
Mrs Williams is believed to be the youngest mother of conjoined twins in Britain.
She and her husband found out about their children's condition at a routine 12-week scan.