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In this paper, we discuss a method to conduct a quantitative study of thestar 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 samekind of galaxies using ground-based observations. It is based on the comparisonof observed CMDs with a set of model CMDs. The latter are computed assumingdifferent evolutionary scenarios, and include a detailed simulation ofobservational effects. HST CMDs are ~3 mags deeper than typical ground-basedCMDs, allowing the observation, for all LG galaxies, of a part of the CMD thatup till now had remained accessible only for the very nearest galaxies. A veryimportant feature that will become accessible is the HB+red-clump. Thedistribution of stars along this structure is quite sensitive to age andmetallicity and should provide a very important improvement in the timeresolution of the SFH for stars older than ~2-3 Gyr. We show and discuss fourmodel CMDs which would be comparable with CMDs from deep HST observations.These model CMDs represent the following evolutionary scenarios correspondingto a wide range of dwarf galaxy sub-types from dI to dE: A) a constant SFR from15Gyr 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 range15-12 Gyr. In all four cases a range of metallicity from Z=0.0001 to Z=0.004has been assumed. The present analysis is just a first qualitative approach towhat one may expect to find in the CMDs of LG galaxies. However a complete setof model CMDs must be computed to analize the data for each galaxy, using thecrowding effects derived for that particular galaxy.Comment: 2 fi

Erratum: "Model Color-Magnitude Diagrams for Hubble Space Telescope Observations of Local Group Dwarf Galaxies" (ApJ, 469, L97 [1996])