According to research in the Netherlands, 40% of twins develop their own language, or idioglossia as it's called (I thought that's what George Bush spoke), but grow out of it as they start to converse with a wider range of adults and children.
It raises interesting questions about the influence of interaction and the nature of children's language acquisition. Whose input has the most influence? Do twins get more input but of lower "quality" (a bit like Chomsky's poverty of the stimulus idea) because they hear each others' language more? According to the National Literacy Trust website there are various reasons for twins developing language in different ways:
Late onset of speech, and speech and language difficulties, including stuttering, are more common in twins than in singletons. This is because twins are frequently premature or low birth weight babies, and their parents may have less time to attend to them individually and to help them develop verbal skills... They used simple language and fewer words when they talked to each other. A British study showed that twin language is higher (around 50%) in twins with speech and language difficulties than for twins with normal language (11%).
I've not noticed my own twin sons speaking like this, but they do have a weird telepathy sometimes and know just when to get on the computer whenever I want to update this blog.
Meanwhile, here are some links to research and advice on twin speech:
First words on twin speech
Wikipedia - idioglossia
National Literacy Trust on twin language
ENA1 - Child Language Acquisition
EA4C - Language Investigation (potential investigations could include comparative analysis of twins' language against singletons' language, or even analysis of differences between siblings)