Quasielastic neutron scattering experiments (time-of-flight, neutron spin echo, and backscattering) on protonated poly(vinyl methyl ether) (PVME) have revealed the hydrogen dynamics above the glass-transition temperature. Fully atomistic molecular dynamics simulations properly validated with the neutron scattering results have allowed further characterization of the atomic motions accessing the correlation functions directly in real space. Deviations from Gaussian behavior are found in the high-momentum transfer range, which are compatible with the predictions of mode coupling theory (MCT). We have applied the MCT phenomenological version to the self-correlation functions of PVME atoms calculated from our simulation data, obtaining consistent results. The unusually large value found for the λ-exponent parameter is close to that recently reported for polybutadiene and simple polymer models with intramolecular barriers.