We consider functions f(. A, B) of noncommuting self-adjoint operators A and B that can be defined in terms of double operator integrals. We prove that if f belongs to the Besov class B∞,11(R2), then we have the following Lipschitz-type estimate in the trace norm: {norm of matrix}f(A1,B1)-f(A2,B2){norm of matrix}S1≤const({norm of matrix}A1-A2{norm of matrix}S1+{norm of matrix}B1-B2{norm of matrix}S1). However, the condition f∈B∞,11(R2) does not imply the Lipschitz-type estimate in the operator norm.