In this paper , we discuss a method to conduct a quantitative study of the star formation history ( SFH ) of Local Group ( LG ) galaxies using Hubble Space Telescope ( 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 .

CMDs obtained with HST are \sim 3 mags deeper than typical CMDs obtained from ground-based telescopes , 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 with HST is the horizontal-branch plus the 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 \simeq 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 15 Gyr 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 10-9 Gyr 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 .