But neither child wants to leave her home and the parents they think of as their own.
The truth about the girls' identities only emerged after the ex-husband of one mother refused to pay support for his daughter because she looked nothing like him.
The case went to court in the Ural Mountains town of Kopeisk, DNA tests were ordered, and the results showed the child was not related to the parents.
"We did two DNA tests," one mother Yuliya Belyaeva has said. "Both tests showed that neither my ex-husband nor I were Irina's biological parents.
"The judge couldn't believe it. She said she'd only seen cases like this on TV and didn't know what to advise us."
Belyaeva recalled that when she gave birth to her daughter in December 1998, another woman had been in labour in the same ward.
That woman was discovered on the other side of town - along with her daughter.
"It was true," Belyaeva said. "Their daughter, Anya, was blond and looked just like me and my ex-husband. And our daughter was dark-skinned and had dark hair and looked like the other father.
"Suddenly my whole world turned upside down and inside out."
But neither child wants to leave home.
"Irina keeps saying to me, 'Mum, please don't give me away!'" Belyaeva said. "I comfort her by saying, 'I would never do anything against your wishes. Nothing has changed. I'm still your mother.'
"As for Anya, my biological daughter, she also says she wants to remain with the parents she knows. She will just visit from time to time."
Both families are now suing the hospital for the mix-up.
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