  We constructed diagnostic diagrams using emission line ratios and equivalent
widths observed in several samples of HII galaxies. The diagrams are compared
to predictions from new photoionization models for evolving starbursts. We find
that HII galaxies from objective-prism surveys are not reproduced by models of
instantaneous starbursts surrounded by constant density, ionization bounded HII
regions. The observed relations between emission line ratios and Hb equivalent
width (W(Hb)) can be understood if older stellar populations are not negligible
in HII galaxies. Also, different dust obscuration for stars and gas and leakage
of Lyman continuum photons from the observed HII regions can be important. As a
result, HII galaxies selected from objective-prism surveys are unlikely to
contain many objects in which the most recent starburst is older than about
5~Myr. The observed increase of [OI]/Hb with decreasing W(Hb) can result from
the dynamical effects of winds and supernovae. This interpretation provides
also a natural explanation of the small range of ionization parameters in giant
HII regions. The [OIII]/Hb vs [OII]/Hb diagnostic diagram cannot be fully
understood in terms of pure photoionization models and indicate the need for
additional heating sources. The [NII]/[OII] ratio is shown to increase as W(Hb)
decreases. A possible explanation is an N/O increase due to gradual enrichment
by winds from Wolf-Rayet stars on a time scale of 5 Myr. (abridged abstract)
