  I examine the possibility that the Cold Neutral Medium of the interstellar
medium in galaxies contains a molecular gas phase that may represent a
significant and even the dominant amount of its mass in metal-poor regions. In
spiral galaxies such regions are found at large galactocentric distances where
diffuse H$_2$ gas will be untraceable through its feeble $ ^{12}$CO J=1--0
emission, the very lack of it being also responsible its higher kinetic
temperatures ($\rm T_k\sim 60-100$ K). Sensitive sub-mm imaging of spiral
galaxies has demonstrated the existence of dust well inside their HI gas
distribution while recent observational work suggests a high H$_2$ formation
rate from HI association onto grains. The latter is indeed a critical unknown
and a high value can easily compensate for the reduction of the available grain
surface in the metal-poor environments giving rise to a CO-poor, diffuse H$_2$
phase that may then contribute significantly to the mass and pressure of the
interstellar medium in such environments.
