  (Abridged.) We present one-zone chemical evolution models for two dwarf
starburst galaxies, NGC 1705 and NGC 1569. Using information about the past
star formation history and initial mass function of the systems previously
obtained from Hubble Space Telescope colour-magnitude diagrams, we identify
possible scenarios of chemical enrichment and development of galactic winds. In
order not to overestimate the current metallicity of the interstellar gas
inferred from H II region spectroscopy, we suggest that the winds efficiently
remove from the galaxies the metal-rich ejecta of dying stars. Conversely,
requiring the final mass of neutral gas to match the value inferred from 21-cm
observations implies a relatively low efficiency of interstellar medium
entrainment in the outflow, thus confirming previous findings that the winds
driving the evolution of typical starbursts are differential. These conclusions
could be different only if the galaxies accrete huge fractions of unprocessed
gas at late times. By assuming standard stellar yields we obtain a good fit to
the observed nitrogen to oxygen ratio of NGC 1569, while the mean N/O ratio in
NGC 1705 is overestimated by the models. Reducing the extent of hot bottom
burning in low-metallicity intermediate-mass stars does not suffice to solve
the problem. Localized self-pollution from stars more massive than 60 MSun in
NGC 1705 and/or funneling of larger fractions of nitrogen through its winds are
then left to explain the discrepancy between model predictions and
observations. Inspection of the log(N/O) vs. log(O/H)+12 diagram for a sample
of dwarf irregular and blue compact dwarf galaxies in the literature favours
the latter hypothesis.
