  Dwarf irregular and blue compact galaxies are very interesting objects since
they are relatively simple and unevolved. We present new models for the
chemical evolution of these galaxies by assuming different regimes of star
formation (bursting and continuous) and different kinds of galactic winds
(normal and metal-enhanced). Our results show that in order to reproduce all
the properties of these galaxies, including the spread in the chemical
abundances, the star formation should have proceeded in bursts and the number
of bursts should be not larger than 10 in each galaxy, and that metal-enhanced
galactic winds are required. A metal-enhanced wind efficiency increasing with
galactic mass can by itself reproduce the observed mass-metallicity relation
although also an increasing efficiency of star formation and/or number and/or
duration of bursts can equally well reproduce such a relation. Metal enhanced
winds together with an increasing amount of star formation with galactic mass
are required to explain most of the properties of these galaxies. Normal
galactic winds, where all the gas is lost at the same rate, do not reproduce
the features of these galaxies. We suggest that these galaxies should have
suffered a different number of bursts varying from 2 to 10 and that the
efficiency of metal-enhanced winds should have been not too high
($\lambda_{mw}\sim1$). We predict for these galaxies present time Type Ia SN
rates from 0.00084 and 0.0023 per century. Finally, by comparing the abundance
patterns of Damped Lyman-$\alpha$ objects with our models we conclude that they
are very likely the progenitors of the present day dwarf irregulars. (abridged)
