We present the results of a detailed molecular dynamics study of poly(ethylene-oxide) (PEO) NaI polymer electrolytes. We focus on the influence of the salt on the dynamics of the polymer segments. This is done by calculating the mean square displacements of the CH2 groups and comparing the corresponding self-part of the intermediate scattering function with neutron spin-echo experiments. Three different systems are studied: pure PEO, PEO-NaI with reduced ion charges, and PEO-NaI with harmonic springs between the O atoms and Na ions. Simulations of pure PEO are in good agreement with the experimental results, indicating the validity of the PEO model. In the polymer electrolyte, a slowing down is observed in both the PEO-NaI models. Adding harmonic springs between Na and O results in a better agreement with neutron spin-echo experiments. It also affects the k dependence of the relaxation times of F(k,t), changing from v = 3.3 to v = 4.0 (tau similar to k(-v)). This is also observed in experiments.