The time kinetics of the vibrational relaxation of excimers is studied in the diffusional approximation. Simple formulae for functions of nonstationary vibrational distribution are found for the electronically excited molecules. Some spectral-kinetic dependencies of the excimer luminescence are explained in a new way. The possibilities of the determination of excimer parameters are discussed. The dependence of energetical characteristics of excimer lasers on these parameters is particularly emphasized. (author). 22 refs, 5 figs.