The temporal evolution of rates and probabilities of transitions, induced by light between states of a molecule interacting with a dissipative medium, are derived for a Hamiltonian containing an anti-Hermitian term which describes dissipation. Our theoretical treatment introduces a biorthonormal basis set of decaying eigenstates to obtain the rates and probabilities from perturbation theory. The formalism is developed for excitation by continuous and pulsed light. As an example, it is applied to the excitation of molecules adsorbed on solid surfaces, taking into account the dissipation of energy into the solid as the molecule relaxes or is desorbed. (C) 2001 American Institute of Physics.