The high pressure structural behavior of H2 and Ne clathrate hydrates with approximate composition H2/Ne·~4H2O and featuring cubic structure II (CS-II) was investigated by neutron powder diffraction using the deuterated analogues at ~95 K. CS-II hydrogen hydrate transforms gradually to isocompositional C1 phase (filled ice II) at around 1.1 GPa but may be metastably retained up to 2.2 GPa. Above 3 GPa a gradual decomposition into C2 phase (H2·H2O, filled ice Ic) and ice VIII’ takes place. Upon heating to 200 K the CS-II to C1 transition completes instantly whereas C1 decomposition appears sluggish also at 200 K. C1 was observed metastably up to 8 GPa. At 95 K C1 and C2 hydrogen hydrate can be retained below 1 GPa and yield ice II and ice Ic, respectively, upon complete release of pressure. In contrast, CS-II neon hydrate undergoes pressure-induced amorphization at 1.9 GPa, thus following the general trend for noble gas clathrate hydrates. Upon heating to 200 K amorphous Ne hydrate crystallizes as a mixture of previously unreported C2 hydrate and ice VIII’.