[en] A nonthermal model for power-law X-ray and gamma-ray sources is considered. An initial, primary distribution of relativistic electrons is injected and cooled via Compton scattering of soft photons (produced either externally or by the synchrotron mechanism). The scattered photons, constituting a primary gamma-ray source, produce electron-positron pairs that act as a secondary electron injection, which in turn produce a secondary photon spectrum. Pairs formed by a part of the photon spectrum optically thin to pair production are taken into account. The distribution of particles and photons is obtained, and numerical results as well as analytical solutions to certain special cases are presented. For the case of a delta-function primary electron injection it is found that the photon spectrum in the X-ray region is well approximated by a power law, with the energy spectral index alpha(X) lying in the relatively narrow range 0.5-0.9 as the compactness parameter L(x)/R (where L(x) is the X-ray luminosity and R is the source radius) varies over many orders of magnitude. This is proposed as a possible mechanism to explain the universal X-ray spectra observed from active galactic nuclei. 20 references