  We present models of the evolution of the gaseous and stellar content of
galaxies incorporating the formation of H_2 out of HI gas as part of such a
model. We do so by formulating a subgrid model for gas clouds that uses
well-known cloud scaling relations and solves for the HI-H_2 balance set by the
H_2 formation on dust grains and its FUV-induced photodissociation by the
temporally and spatially varying interstellar radiation field. This allows the
seamless tracking of the evolution of the H_2 gas phase, its precursor Cold
Neutral Medium (CNM) HI gas, simultaneously with the star formation. Our most
important findings are: a) a significant dependence of the HI-H_2 transition
and the resultant H_2 gas mass on the ambient metallicity and the H_2 formation
rate, b) the important influence of the characteristic star formation timescale
(regulating the ambient FUV radiation field) on the equilibrium H_2 gas mass
and c) the possibility of a diffuse H_2 gas phase. Finally, we implement and
briefly explore a novel approach of using the ambient H_2 gas mass fraction as
a criterion for the onset of star formation. (abridged)
