The purpose of this paper is to obtain an integral representation for the difference f(L ₁ )-f(L ₂ ) of functions of maximal dissipative operators. This representation in terms of double operator integrals will allow us to establish Lipschitz-type estimates for functions of maximal dissipative operators. We also consider a similar problem for quasicommutators, i.e., operators of the form f(L ₁ )R - Rf(L ₂ ).