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A discussion is given of the properties of the strong nonthermal radio sources and particularly of those of extragalactic origin. These sources radiate by the synchrotron process. The properties of the galaxies associated with the sources are described. A review is then given of the various theoretical proposals which have been made to try to explain how the generation of very large fluxes of relativistic particles (with total energies Â¿ 10660 ergs) in very short times (~106 years or less) has taken place. Finally, the requirements which must be fulfilled for a satisfactory theory of the origin of such sources are outlined.