Sergei Naboko and Roman Romanov Spectral Singularities and Asymptotics of Contractive Semigroups. I. (66K, LaTeX 2e) ABSTRACT. The problem of localization of spectral singularities of dissipative operators in terms of the asymptotic of the corresponding exponential function is studied. We give a solution to this problem for the singularities of higher orders in the frame of the perturbation theory.