The radio continuum spectra of 14 star-forming galaxies are investigated by fitting nonthermal (synchrotron) and thermal (free-free) radiation laws. The underlying radio continuum measurements cover a frequency range of ~325 MHz to 24.5 GHz (32 GHz in case of M82). It turns out that most of these synchrotron spectra are not simple power-laws, but are best represented by a low-frequency spectrum with a mean slope alpha_nth = 0.59 +/- 0.20 (S_nu ~ nu^-alpha), and by a break or an exponential decline in the frequency range of 1 - 12 GHz. Simple power-laws or mildly curved synchrotron spectra lead to unrealistically low thermal flux densities, and/or to strong deviations from the expected optically thin free-free spectra with slope alpha_th = 0.10 in the fits. The break or cutoff energies are in the range of 1.5 - 7 GeV. We briefly discuss the possible origin of such a cutoff or break. If the low-frequency spectra obtained here reflect the injection spectrum of cosmic-ray electrons, they comply with the mean spectral index of Galactic supernova remnants. A comparison of the fitted thermal flux densities with the (foreground-corrected) Halpha fluxes yields the extinction, which increases with metallicity. The fraction of thermal emission is higher than believed hitherto, especially at high frequencies, and is highest in the dwarf galaxies of our sample, which we interpret in terms of a lack of containment in these low-mass systems, or a time effect caused by a very young starburst.
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