The rotational motion of the ester methyl group in poly(methyl methacrylate) (PMMA) was investigated using quasielastic neutron scattering (QENS). A comparison between our results and the QENS data reported in the literature for PMMA-d(5) indicates that the amount of quasielastic broadening is highly dependent upon the energy resolution of the spectrometer. This anomalous behavior is here attributed to the method of analysis, namely, the use of a single rotational frequency. Such a procedure leads to a non-Arrhenius temperature dependence, to a temperature-dependent elastic incoherent structure factor, and to values of rotational frequency which are resolution dependent. We propose an alternative approach to the analysis of the QENS data which accounts for the existence of a distribution of rotational frequencies. The frequency data are Fourier transformed to the time domain, and the intermediate scattering function is fitted using a stretched exponential or Kohlraush-Williams-Watts function. The excellent overlap between data from different spectrometers leaves no doubt on the adequacy of our procedure. Measurements of the ether methyl group rotation in poly(vinyl methyl ether) (PVME) are also reported. The PVME data confirm that the behavior observed for PMMA-d(5) is likely to be a common feature to all polymeric systems.