Nine babies born to a Malian woman will need to spend "two to three months" in incubators, a director of the clinic where they were born has said.
Professor Youssef Alaoui of the Ain Borja clinic in Casablanca, Morocco, told the AFP news agency that the case was "extremely rare" and "exceptional".
The mother, Halima Cissé, 25, and her nonuplets - five girls and four boys - are said to be doing well.
The babies weighed between 500g and 1kg (1.1lb and 2.2lb) when they were born.
Medical director Prof Alaoui said that Ms Cissé was 25 weeks pregnant when she was admitted and his team managed to extend her term to 30 weeks. Ten doctors and 25 paramedics assisted at the delivery.
As far as he was aware Ms Cissé had not used any fertility treatments, Prof Alaoui told the Associated Press.
He told BBC Arabic that she had been in a serious condition to begin with because of heavy bleeding, which was brought under control.
"The mother is now in a good condition she's not in danger any more. We wish her and the babies a speedy recovery," he said.
Doctors in Mali conducted ultrasounds and initially believed that she was expecting seven babies. They sent her to Morocco where there are better medical facilities.
After five weeks at the Moroccan clinic, she gave birth by Caesarean section on Tuesday, Fanta Siby, Mali's health minister said.
The minister congratulated the medical teams in Mali and Morocco for the "happy outcome".
Ms Cissé's husband, Adjudant Kader Arby, is still in Mali with the couple's older daughter. He says he has been in touch with his wife in Morocco and is not worried about the family's future.
"God gave us these children. He is the one to decide what will happen to them. I'm not worried about that. When the almighty does something, he knows why," he told BBC Afrique.
Two sets of nonuplets have previously been recorded - one born to a woman in Australia in 1971 and another to a woman in Malaysia in 1999 - but none of the babies survived more than a few days.
A woman who had eight babies in the US in 2009 holds the Guinness World Record for the most children delivered at a single birth to survive. Nadya Suleman's octuplets have grown up and are now 12 years old. She conceived them through in vitro fertilisation.