  We present a UV to mid-IR spectral energy distribution study of a large
sample of SDSS DR13 HII galaxies. These are selected as starburst (EW(H$\alpha)
> 50$\AA) and for their high excitation locus in the upper-left region of the
BPT diagram. Their photometry was derived from the cross-matched GALEX, SDSS,
UKDISS and WISE catalogues.
  We have used CIGALE modelling and SED fitting routine with the
parametrization of a three burst star formation history, and a comprehensive
analysis of all other model parameters. We have been able to estimate the
contribution of the underlying old stellar population to the observed
equivalent width of H$\beta$ and allow for more accurate burst age
determination.
  We found that the star formation histories of HII Galaxies can be reproduced
remarkably well by three major eras of star formation. In addition, the SED
fitting results indicate that: i) in all cases the current burst produces less
than a few percent of the total stellar mass: the bulk of stellar mass in HII
galaxies have been produced by the past episodes of star formation; ii) at a
given age the H$\beta$ luminosity depends only on the mass of young stars
favouring a universal IMF for massive stars; iii) the current star formation
episodes are {\it maximal} starbursts, producing stars at the highest possible
rate.
