A detailed insight into the star formation history of a sample of HII galaxies has been obtained, based on radio continuum and optical broad band and narrow band observations. HII galaxies are dwarf galaxies whose optical spectrum resembles that of HII regions, many of which are also known as Blue Compact Dwarf Galaxies. VLA observations at several radio continuum frequencies revealed unusually shaped radio spectra; most of them displaying a flattening at low frequencies. Several mechanisms are discussed to explain the spectra (Deeg et al., 1992, submitted to ApJ). They are radio absorption mechanisms and cosmic ray (CR) electron loss mechanisms, the latter being important, as CR electrons emit synchrotron radio emission in galactic magnetic fields. Modelling the radio spectra with these mechanisms allowed us to determine parameters such as the magnetic field strength, the electron density, the emission measure as well as the history of the injection of CR electrons into the ISM. These CR electrons are thought to come from supernova remnants of short lived O-stars. Since some of the mechanisms can not be unambiguously distinguished using the radio continuum spectra alone, observations at other wavelengths were needed. CCD images of the complete sample were taken through Hα and broad band B, R, and I filters. The Hα images have been used to derive the current starformation rate and the abundance of O stars. They also allow an independent estimate of the emission measure, whereas the size of the HII regions sets constraints on the effectiveness of free-free radio absorption. Color photometry based on the broad band images was used to derive the stellar population and to estimate the history of the star formation rate by comparison with stellar synthesis models (e.g. Kruger et al., 1991, A&A, 242, 343). The starburst ages derived this way come out to be much older than from the modelling of the radio spectra. More detailed cosmic ray propagation models are used to explain the discrepancy between these ages. Also, the parameter space on which the results are based is investigated in more detail.