The present analytical study using thermodynamic methods for analysis of data from a number of theoretical and experimental works, devoted to the current problem of thermodynamic stability and related thermodynamic characteristics of the following graphene layers systems: 1) double-side hydrogenated graphene of composition CH -theoretical graphane (Sofo et al. 2007) and experimental graphane (Elias et al. 2009); 2) theoretical single-side hydrogenated graphene of composition CH; 3) theoretical single-side hydrogenated graphene of composition C 2 H -graphone; 4) experimental hydrogenated epitaxial graphene, bilayer graphene and a few layers of graphene on SiO 2 or other substrates; 5) experimental and theoretical single-external side hydrogenated single-walled carbon nanotubes, and experimental hydrofullerene C 60 H 36 ; 6) experimental single-internal side hydrogenated (up to C 2 H or CH composition) graphene nanoblisters with intercalated high pressure H 2 gas inside them, formed on a surface of highly oriented pyrolytic graphite or epitaxial graphene under the atomic hydrogen treatment; and 7) experimental hydrogenated graphite (multigraphene) nanofibers with intercalated solid H 2 nano-regions inside them. The main target of the present study is to show a possible breakthrough in solving the problem of hydrogen on-board storage in fuel cell powered vehicles (Nechaev -2012.