The temperature dependence of the low frequency internal friction (LFI
F) and the dynamic shear modulus f2 in polycrystalline samples of meth
ane is studied at 5-85 K. The sharp peak of LFIF and the change of she
ar modulus are discovered at the temperatures 60-70 K. It is assumed t
hat the above anomalies are due to the transition of the methane molec
ules from retarded rotation at T < 60 K to free rotation at T > 60-70
K. It is found that the increase in the N2 content shifts this transit
ion to higher temperatures. The peak of the internal friction and the
growing LFIF background near temperature 20.48 K are connected with th
e beginning and end of the betaalpha phase transition, which is due to
the orientational ordering of the methane molecules. It is supposed t
hat the LFIF background growth below 20 K and LFIF peak in the interva
l 10-15 K are caused by quantum relaxational processes, which are conn
ected with the spin conversion in CH4. The above LFIF anomalies are ex
plained in terms of the dynamic behavior of the methane molecules.