Quasielastic neutron scattering by employing a combination of time-of-flight and backscattering techniques is carried out to explore the molecular mobility of a polymer of intrinsic microporosity (PIM-1) on microscopic timescales in comparison with a high-performance polyimide. Molecular fluctuations can change the structure of the temporary network of micropores and open or close pathways for gas molecules. Therefore, the investigation might help to understand the selectivity of PIMs in gas separation processes. The performed neutron scattering experiments provide evidence for a low-temperature relaxation process, which was assigned to methyl group rotation. This methyl group rotation was analyzed in terms of jump diffusion in a threefold potential. The analysis results in a fraction of methyl groups, which are immobilized. For PIM-1, it was found that the fraction of immobilized methyl groups decreases with increasing temperature up to 350 K. At higher temperatures, the number of immobilized methyl group increases gain due to an underlying relaxation process. This motional process on a somewhat larger length scale might lead to a reversible structural rearrangement, which partially hinders the strongly localized methyl group rotation. In addition, it was found that the activation energies for the methyl group rotation for PIM-1 and the polyimide are significantly higher than that for conventional polymers.