An Italian woman is due to give birth in a hospital in Rome this week to a baby girl - before returning three months later to have triplets.
If both deliveries are successful, it is thought that this will be the first such case in history.
Flavia D'Angelo, aged 20,denied suggestions that she might have had hormone or fertility treatment.
She has already named her first child Denise.
"When I was at the sixth month of my pregnancy and went to see the doctor for the usual tests and scans, he noticed that, apart from Denise, there were another three babies," she said.
"I didn't believe it at first. I remember asking the doctor to make sure because I just couldn't understand how it was possible."
Professor Ian Craft of the London Fertility Clinic said it should not theoretically be possible for a woman to be pregnant twice at the same time.
"Normally when you are pregnant you switch off your ovulation, and you don't then ovulate again and you have no periods until your child is born and you are at least part the way through breastfeeding.
"I have never seen it in my whole professional career."
Professor Craft said the condition, known technically as superfecundation, occurred rarely in animals.
He said it was unheard of for a woman to conceive naturally and then to spontaneously ovulate three eggs again.
The chance of having triplets was only one in 6000, he said, but there was a high risk the triplets would be born prematurely.
