We consider functions of pairs of noncommuting contractions on Hilbert space and study the problem as to which functions we have Lipschitz type estimates in Schatten-von Neumann norms. We prove that if belongs to the Besov class of analytic functions in the bidisc, then we have a Lipschitz type estimate for functions of pairs of not necessarily commuting contractions in the Schatten-von Neumann norms. On the other hand, we show that for functions in, there are no such Lipschitz type estimates for, nor in the operator norm.