A chemical evolution model following the evolution of the abundances o
f He, C, N, O and Fe for the metal poor galaxy IZw 18 is presented. Th
is model takes into account detailed nucleosynthesis and rates of supe
rnovae of type II and I, and assumes that a mass outflow is developed
as a consequence of supernova explosions. The star formation is assume
d to have proceeded in short but intense bursts, so that supernovae of
type II are the main responsible for the mass removal. In this framew
ork we made the hypothesis that the star forming region mainly looses
the nucleosynthesis products of supernovae of type II with the consequ
ence of removing a part of the newly produced oxygen but not the newly
produced He and N. By comparison with the spectroscopic properties of
the HII region we conclude that IZw 18 must have experienced not more
than two bursts of star formation with duration no longer than 10-20
Myr, and that a substantial fraction of primary nitrogen should have b
een produced by massive stars. By comparison with new HST data referri
ng to the HI region, suggesting an oxygen abundance lower by a factor
of 30 than in the HII region, we conclude that the observed abundance
is compatible, inside the observational errors, either with only one r
ecent starburst or with two starbursts separated by a gap of at least
1 Gyr. Predictions for the expected abundances of N, Fe and C in the H
I region, which could be checked by looking at NI, FeII and CII, are g
iven. Our results show that a negligible amount of stellar helium has
been produced. We strengthen the importance of IZw 18 and more general
ly extreme metal poor galaxies for the primordial He abundance determi
nation.