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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 I_c) 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 I_c, 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’.