  In this paper, we discuss a method to conduct a quantitative study of the
star formation history (SFH) of Local Group (LG) galaxies using (HST) data.
This method has proven to be successful in the analysis of the SFH of the same
kind of galaxies using ground-based observations. It is based on the comparison
of observed CMDs with a set of model CMDs. The latter are computed assuming
different evolutionary scenarios, and include a detailed simulation of
observational effects. HST CMDs are ~3 mags deeper than typical ground-based
CMDs, allowing the observation, for all LG galaxies, of a part of the CMD that
up till now had remained accessible only for the very nearest galaxies. A very
important feature that will become accessible is the HB+red-clump. The
distribution of stars along this structure is quite sensitive to age and
metallicity and should provide a very important improvement in the time
resolution of the SFH for stars older than ~2-3 Gyr. We show and discuss four
model CMDs which would be comparable with CMDs from deep HST observations.
These model CMDs represent the following evolutionary scenarios corresponding
to a wide range of dwarf galaxy sub-types from dI to dE: A) a constant SFR from
15Gyr ago to the present time; B) as A), but with the SFR stopped 0.5 Gyr ago;
C) a constant SFR in the age range 10-9Gyr and D) as C) but in the age range
15-12 Gyr. In all four cases a range of metallicity from Z=0.0001 to Z=0.004
has been assumed. The present analysis is just a first qualitative approach to
what one may expect to find in the CMDs of LG galaxies. However a complete set
of model CMDs must be computed to analize the data for each galaxy, using the
crowding effects derived for that particular galaxy.
