Summary: In powerful cosmic nonthermal radiation sources with dominant magnetic-field self generation, the generation of magnetic fields at almost equipartition strength by relativistic plasma instabilities operates as fast as the acceleration or injection of ultra-high energy radiating electrons and hadrons in these sources. Consequently, the magnetic field strength becomes time-dependent and adjusts itself to the actual kinetic energy density of the radiating electrons in these sources. This coupling of the magnetic field and the magnetic field energy density to the kinetic energy of the radiating particles changes both the intrinsic temporal evolution of the relativistic particle energy spectrum after injection and the synchrotron and synchrotron self-Compton emissivities.