Article is devoted to a problem of interaction of legal systems of the world. The author draws a conclusion about existence the Muslim legal system; the liberal-post social capitalist system and the system of law of totalitarian socialism. He notes that the convergence of global legal systems is growing, but this has its objective limits. So far in Muslim, liberal-capitalist, and totalitarian socialist systems there are constitutional provisions which can never be accepted by other systems because such provisions are irreconcilable, antagonistic.