A sample of HII galaxies has been observed in several radio and optical bands. These galaxies are undergoing very active star formation; they have been selected on the basis of strong radio continuum emission. Radio continuum observations were obtained to determine their radio spectra. Several of the spectra were found to flatten towards lower frequencies, which is unusual. Surface and aperture photometry was obtained in the B,R, and I bands and in the Hα emission line. Several mechanisms which could shape the radio spectra are reviewed towards their suitability to account for the spectral shapes and are fitted to the spectra. The equipartition magnetic field was found to be 10-30 mu G, and the radiation density inside HII regions was found to be between 2 and 15 eV cm(-3) . The spectra resulting from a time variable relativistic electron injection ('synchrotron aging') show variations of the injection rate within a few Myrs. A fit based on free-free absorption balances free-free absorption and thermal emission, constraining the maximum size of the HII region. This allows a direct comparison with Hα observations, showing sizes of 0.5 - 1 kpc. The fits also gave the electron density of 10 - 60 cm(-3) , and the emission measure of the order 10(5) pc cm(-6) . A correlation between the galaxies' fraction of thermal emission and their size and radio luminosity was found. A model describing electron diffusion losses, dependent on a galaxies' size, can reproduce the correlation well. Radio and FIR emission indicate star formation rates which are enhanced during the last 10(6-7) years. Star formation ages derived from 'synchrotron aging' are compared to those derived from optical colors and the radio-to-FIR ratio, establishing 'synchrotron aging' as a valid indicator for these ages. This allowed to sort the galaxies into an age sequence of their starbursts. The physical picture of a region in which star formation, SN explosions, and the resulting nonthermal radio emission takes place, can be accounted for well, by comparing the different star formation estimators which are based on a variety of radiative processes.