ABSTRACT: We present the results of an investigation of acceleration processes in galactic centers and show that a quasi-monoenergetic electron distribution (pile-up) forms in quite a natural way under the combined action of diffusive shock wave acceleration, stochastic acceleration on turbulent MHD waves and radiation losses. We follow the temporal evolution of both the electron and the photon distribution. This requires the numerical solution of two kinetic equations, i.e., a fully coupled set of nonlinear partial integro-differential equations. We apply the results to the non-thermal radio emission from the Galactic Center source Sgr A^*, which we interpret as being optically thin synchrotron radiation from these quasi-monoenergetic electrons.