We determined the self part of the intermediate scattering function in liquid polyethyleneoxide (PEO) and PEO-alkali iodide complexes by means of neutron spin-echo spectroscopy and molecular dynamics (MD) computer simulations. We present the first accurate quantitative results on the segmental dynamics in the time range up to 1 ns and the wave-vector range from a few nm(-1) to approximately 20 nm(-1). We investigate the influence of polymer chain length, salt concentration, and cation type. We find that the neutron data and MD data for pure PEO agree very well. A relatively small concentration of dissolved salt (1 metal ion per 15 monomers) leads to a slowing down of the segmental motions by an order of magnitude. Here, the MD simulations agree qualitatively. Increasing the chain length from 23 to 182 monomers has no significant effect except at the highest salt concentration. Similarly, changing the cation from Li to Na hardly makes any difference. The Rouse model does not adequately describe our data.