Stability regions of crystal phases in the water–hydrogen system have been studied within our statistical thermodynamic model for describing clathrate compounds. The thermodynamic stability of hydrogen-containing ices I h (C 0 Ih ), II (C 1 ), I c (C 2 ), classical clathrate hydrogen hydrate CS-II, and new hydrogen-filled ice phase C 0 has been analyzed. It has been shown that all considered phases are thermodynamically stable, but phase C 0 is metastable with respect to the other phases. The chemical potentials of water molecules in phases C 0 and C 1 are close to each other. As a result, metastable phase C 0 is experimentally observed in the stability region of phase C 1 .