Pregnant Christine Bolden, 26, collapsed and was taken to hospital at the beginning of March but despite medics' efforts she was declared brain-dead five days later.
Her family pleaded with the doctors to save Christine's unborn babies and, almost miraculously, twins Nicholas and Alexander were born by Caesarean section a month after their mum was put on a respirator.
The boys were born 25 weeks premature on April 5 and remain on ventilators at a children's hospital in Grand Rapids, Michigan, U.S., according to reports.
Hospital spokesman Bruce Rossman said. "We certainly hope they make it, but at this time they're too young to make a confident prognosis.
"Children born this early will be at high risk for chronic conditions. It's too soon to tell."
Mr Rossman said the babies had to get to at least 24 weeks before they could consider delivery.
Dr. Cosmas Vandeven, who specialises in high-risk pregnancies at the University of Michigan hospital, told the Associated Press that Christine's case is a "very exceptional scenario."
An important ethical issue in cases like these, he said, is whether a brain-dead woman would suffer by being kept on a respirator and undergoing a C-section.
"Almost every parent would give their life for their child," Vandeven said.
"But you need to get truly independent opinions: Are we sure we're not causing harm to the mom?"
He said 70 per cent of babies born at 25 weeks survive, but the risk for long-term health problems is high.