[en] Consideration is given to a model of gamma-ray burst sources based on repeated Compton scatterings of soft photons by relativistic nonthermal electrons. Relativistic electrons which are continuously produced in the source radiate the total power L supplied to them. Higher order Compton scatterings, which occur when L(soft) is much less than L make the model distinct. The spectrum having an X-ray energy index of about one results from the superposition of the spectral components from several orders of Compton scattering; the change of the slope at several hundred keV arises from the Klein-Nishina decline of the scattering cross section. 15 references