The content of gas in galaxies with an anomalously high relative mass of hydrogen $M_{HI}/M_*$ for a given mass of the stellar population $M_*$ (VHR-galaxies) is considered, using the available samples of such galaxies. It is shown that, within the optical diameter $D_{25}$, the mass of HI in VHR galaxies, as well as in galaxies with "normal" HI content, is limited by a value that depends on the specific angular momentum of the disk. Outer gaseous disks beyond $D_{25}$, which contain the main amount of HI in most of the galaxies we consider, are gravitationally stable, and, as a rule, they retain an approximately constant value of the stability parameter $Q_{gas}$ over a large range of radial distances. It allows to propose that the outer disks of VHR galaxies are not recently acquired, but are of great age, and their gravitational instability was the main regulator of star formation during their formation. In this case, the extended disks of galaxies should also include a low-brightness stellar components of old stars extending far beyond their optical diameter $D_{25}$.