The first possibility is that an egg cell began to divide, without separating, and each budding part was then fertilized with a single sperm. The genes could then have gotten mixed up before the egg fully separated into two.
Likelier, though, is that two sperm cells fused with a single egg, creating an embryo with three sets of chromosomes rather than two.
In this scenario, there was a mixing of genes within the double-fertilized egg. It then split into two cells, and each cell would have shed an unwanted set of chromosomes.
As a result, the children would have identical genes from their mother's side — but would share only half of their genes on their father's side.
The study initially appeared in the Journal of Human Genetics, published in Britain.
A double fertilization of a single egg is not unheard of but until now offspring have never been known to survive.
"It's extremely unlikely that we will ever see another case," said Charles Boklage, an expert on twinning at Eastern Carolina University in North Carolina.
Souter said the case raised intriguing questions about twinning.
"It makes me wonder whether the current classification of twins is an oversimplification," she said.