The restructuring of grammar in situations of intensive language contact is a fairly common phenomenon, and it raises various interesting theoretical questions concerning the changing of human languages. However, as such processes take place over several hundred years, linguists cannot witness them directly, and can only speculate about what induces them and how they proceed. The Uralic languages of Russia present unique evidence in this respect. Under the heavy influence of Russian, their head-final syntax, generating Subject-Object-Verb (SOV) sentences, is being restructured into a head-initial, SVO-type system, and this is happening in an accelerated pace in front of our eyes. Thereby we have the possibility of understanding on the basis of direct evidence how a head-final grammar is rebuilt as a head-initial one, and more generally, how an asymmetrical contact situation affects the grammars of the languages involved.