In this work, data of Rodriguez-Baker et al. and some others were analyzed in relation to the long- term, i.e., about 25 years, problem of “super” storage of “reversible” (at 300 K) hydrogen (~38±10 wt.%, i.e. the atomic ratio (H/C) ≈ 7±3)), along with “irreversible” hydrogen ( ~11±3 wt.% ((H/C) ≈ 1.5±0.4)) in activated graphite nanofibers (GNFs). For a more in-depth study of the above problem, an effective methodology of analyzing the thermal desorption spectra (TDS) of hydrogen was developed and used. Such an analysis of the reported TDS and thermogravimetric data of Rodriguez-Baker et al., relevance to the storage of "irreversible" hydrogen in GNFs, showed the presence of three desorption peaks, including the main peak #1 (~8.4 wt.% ((H/C) ≈1.1)) with the desorption activation energy of about 40 kJ/mol(H2). The physics of "super" storage of hydrogen in GNFs can be based on the hydrogen spillover effect and on the Kurdjumov phenomenon of thermoelastic phase equilibrium. There is a real opportunity to reproduce the above results on the "super" storage of "reversible" hydrogen, but only with the disclosure of the know-how of the technology of activation treatment of GNFs, which ensures the appearance in them the peak # 1.