The heat capacity CP of Kr-nCH4 solid solutions with CH4 concentrations n=0.82, 0.86, and 0.90 and of solutions with n=0.90, 0.95 doped with 0.002 O2 impurity is investigated under equilibrium vapor pressure over the interval 1–24K. The (T,n) phase diagram of Kr-nCH4 solid solutions is refined, and the region of two-phase states is determined. The contribution of the rotational subsystem, Crot, to the heat capacity of the solutions is separated. Analysis of Crot(T) at T<3K makes it possible to estimate the effective conversion times τ and the energy gaps E1 and E2 between the tunneling levels of the A,T and A,E nuclear-spin species of CH4 molecules in the orientationally ordered subsystem and to determine the effective energy gaps E1 between the lowest levels of the A and T species. The relations τ(n) and E1(n) stem from changes of the effective potential field in result of the replacement of CH4 molecules by Kr atoms at sites of the ordered sublattices. The effective gaps EL between a group of tunneling levels of the librational ground state and the nearest group of excited levels of the librational state of the ordered CH4 molecules in the solutions with n=0.90 (EL=52K) and 0.95 (EL=55K) is estimated.