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The high-pressure structural behavior of the noble gas (Ng) clathrate hydrates Ar center dot 6.5 H2O and Xe center dot 7.2 H2O featuring cubic structures II and I, respectively, was investigated by neutron powder diffraction (using the deuterated analogues) at 95 K. Both hydrates undergo pressure-induced amorphization (PIA), indicated by the disappearance of Bragg diffraction peaks, but at rather different pressures, at 1.4 and above 4.0 GPa, respectively. Amorphous Ar hydrate can be recovered to ambient pressure when annealed at >1.5 GPa and 170 K and is thermally stable up to 120 K. In contrast, it was impossible to retain amorphous Xe hydrate at pressures below 3 GPa. Molecular dynamics (MD) simulations were used to obtain general insight into PIA of Ng hydrates, from Ne to Xe. Without a guest species, both cubic clathrate structures amorphize at 1.2 GPa, which is very similar to hexagonal ice. Filling of large-sized H cages does not provide stability toward amorphization for structure II, whereas filled small-sized dodecahedral D cages shift PIA successively to higher pressures with increasing size of the Ng guest. For structure I, filling of both kinds of cages, large-sized T and small-sized D, acts to stabilize in a cooperative fashion. Xe hydrate represents a special case. In MD, disordering of the guest hydration structure is already seen at around 2.5 GPa. However, the different coordination numbers of the two types of guests in the crystalline cage structure are preserved, and the state is shown to produce a Bragg diffraction pattern. The experimentally observed diffraction up to 4 GPa is attributed to this semicrystalline state.