The translational and rotational dynamics of methane in NaY zeolite have been studied by quasi-elastic neutron scattering (QENS) at different temperatures and loadings. The QENS results reveal a marked temperature sensitivity. At 100 K, there is no migration of the methane from cage to cage on the 35-ps time scale of the experiment so that the time spent by a molecule in a supercage is longer than this. At 100 K, 88% of the methane molecules are found to be localized, performing rotational diffusion, and 12% of molecules diffuse in a volume limited by the walls of the supercages. At 150 K, there are no trapped molecules, 44% of methane molecules diffuse between the supercages and 56% diffuse locally within the supercages. At 200 and 250 K, the proportion of mobile molecules and their diffusion coefficients increase. The QENS results are in good agreement with theoretical methods which predict a progressive delocalization of the molecules with increasing temperature. The self-diffusion coefficients determined by QENS are in excellent agreement with the NMR results and, to a lesser extent, with molecular dynamics simulations. The activation energy for self-diffusion is of 6.3 kJ mol(-1).