  A sample of 66 galaxies from the catalog of Bettoni et al. (CISM) with
anomalously high molecular-to-atomic hydrogen mass ratios (M_{mol}/M_{HI}>2) is
considered. The sample galaxies do not differ systematically from other
galaxies in the catalog with the same morphological types, in terms of their
photometric parameters, rotational velocities, dust contents, or the total mass
of gas in comparison with galaxies of similar linear sizes and disk angular
momentum. This suggests that the overabundance of $H_2$ is due to transition of
HI to H_2. Galaxies with bars and active nuclei are found more frequently among
galaxies which have M_{mol} estimates in CISM. In a small fraction of galaxies,
high M_{mol}/M_{HI} ratios are caused by the overestimation of M_{mol} due to a
low conversion factor for the translation of CO-line intensities into the
number of H_2 molecules along the line of sight. It is argued that the
"molecularization" of the bulk of the gas mass could be due 1) to the
concentration of gas in the inner regions of the galactic disks, resulting to a
high gas pressure and 2) to relatively low star-formation rate per unit mass of
molecular gas which indeed takes place in galaxies with high M_{mol}/M_{HI}
ratios.
