The data on the spectrum of the cosmic-ray electron component near the earth, on the radio-spectra of radio-galaxies, quasars and the Crab Nebula, as well as the data pertaining to the X-ray spectrum of the cosmic background, all agree that the sources of cosmic-ray electrons (such as supernovae and galactic nuclei) inject particles characterized by a power spectrumN(E)=KE -γ0, with γ0≃1.5 2.5. A mechanism is known in which the source emits a proton-nuclear component of cosmic rays with a spectrumN n (E)=K n E -γ n, γn = δ + 2, δ=w cr/(w-w cr), wherew cr is the cosmic-ray energy density in the source, andw=w cr+w n+w turb, the total energy density. We obtain γ=2.5 in agreement with observations on the natural assumption that δ=0.5. Within the framework of the same model with some additional assumptions, the electrons in the source, as well as those ejected by the source, are shown to have a power-spectrum characterized with γ0 ≤ γn = δ + 2. Thus the model discussed gives an adequate spectrum for both the proton-nuclear and the electron components of cosmic rays.