Thermodynamic conditions of existence in the p-T plane and the composition of neon hydrates based on ices Ih and II are determined. The occupancy of neon in cages (channels) of ices Ih and II at temperatures below 0°C is calculated. It is shown that the occupancy of neon in hydrate based on ices cages decreases with growing temperature. Lines of monovariant equilibria between gas phase (neon)-neon hydrate based on ice Ih-liquid water (or ice II) and neon-gas phase (neon)-hydrate based on ice II-liquidwater (or ice II) are found. The line of divariant equilibria between neon hydrate based on ice Ih-neon hydrate based on ice II has been also calculated. The possibility of ice stabilization due to inclusion of neon into ice cages (channels) is shown.