  We present evolutionary population synthesis models for the study of the cool
and luminous intermediate age stellar populations in resolved galaxies with
particular emphasis on carbon star populations. We study the effects of the
star formation history, the age and the metallicity on the populations of
intermediate mass stars. In the case of instantaneous bursts, we confirm that
lower metallicity results in higher contribution of carbon stars to the total
star number, and in higher number ratios of carbon stars to late-type M stars.
Chemically consistent models are used to study the effect of the star formation
history on the relations between carbon star population properties and global
parameters of the parent galaxy (age, metallicity). Our models are able to
account, for the first time, for those correlations, as observed in the
galaxies of the Local Group. For stellar populations older than 1 Gyr, the
properties of carbon star populations are linked to the current metallicity in
a way that is quite independent of the star formation scenario. The number of
carbon stars to late-type M stars forms a metallicity sequence along which
stellar populations with very different star formation histories are found
(Abridged).
