  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.
