The temperature dependence of the linear thermal expansion coefficient a(T) has been investigated in the temperature range of 2.5 to 23 K for two different CH 4 -C 60 solutions in which CH 4 molecules occupied 24 and 50% of the octahedral interstitial sites of the C 60 lattice. In both cases, a(T) exhibits hysteresis, suggesting the existence of two types of orientational glass associated with these solutions. The temperature of the first-order phase transition between these two glasses was estimated and the behavior of these two glasses compared. The characteristic times of thermalization t 1 , reorientation of the C 60 molecules t 2 , and of the phase transformation between the glasses t¢, have been estimated for these solutions. Both the temperature dependence of a(T) and the characteristic thermalization time t 1 are found to have features near the phase transition temperature and an explanation has been put forward to explain these observed features.PACS: 74.70.Wz Fullerenes and related materials.