[en] We consider a nonthermal model for power-law X-ray and γ-ray sources. 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 γ-ray source, produce electron-positron pairs that act as a secondary electron injection, which in turn produce a secondary photon spectrum. In contrast to the treatment of this problem presented by Bonometto and Rees in 1971 and Kazanas in 1984, we take into account pairs formed by a part of the photon spectrum optically thin to pair production. We solve self-consistently for the distribution of particles and photons, and present numerical results as well as analytical solutions to certain special cases. For the case of a delta-function primary electron injection we find that the photon spectrum in the X-ray region is well approximated by a power law, with the energy spectral index α/sub X/ lying in the relatively narrow range 0.5--0.9 as the compactness parameter L/sub X//R (where L/sub X/ is the X-ray luminosity and R is the source radius) varies over many orders of magnitude. We propose this as a possible mechanism to explain the universal X-ray spectra observed from active galactic nuclei