  The star formation history (SFH) of the Pegasus dIr, a likely Local Group
member at 0.95 Mpc from the Milky Way, is investigated. We characterize the SFH
by two basic functions: the star formation rate, psi(t), and the chemical
enrichment law, Z(t). It has been derived by comparing the color-magnitude
diagram of the resolved stars in Pegasus, with a total of 189 model diagrams
produced with different psi(t) and Z(t) laws.
  Star formation began in Pegasus about 15 Gyr ago and was larger, on average,
during the first half than during the second half of the galaxy's life. During
the most recent epoch, the star formation seems to be produced in a bursting
mode. This may have been the case for the whole life of the galaxy, although
the resolution in time towards older epochs is not good enough to actually
detect it. As for the chemical enrichment law, the best way to account for the
observed metallicity of the galaxy (Zf=0.002(+0.002/-0.001) is that it suffered
a prompt initial chemical enrichment. This would be the case if infall was
important and points to a picture in which the galaxy began forming stars and
enriching its interstellar medium in an early phase of collapse.
  Pegasus and NGC 6822 are the only dIrs for which the kind of analysis
presented here has been done. The fact that both galaxies show an important old
to intermediate-age stellar population indicates that the Baade's sheet
observed in most dIr, may in fact be the signature of an important population
of old stars and suggest that dIr actually are old objects populated by large
numbers of old stars. The percentage of dark matter in Pegasus turns out to be
92%.
