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The dielectric properties of poly(ethylene oxide)–multiwalled carbon nanotube (MWCNT) nanocomposites have been studied over a wide range of frequency (0.1–106 Hz) and temperature (180–300 K). Nanocomposites were prepared by both melt mixing and twin-screw extrusion, and the concentration of MWCNTs was varied from 0 to 5 wt. %. Both the real and imaginary parts of the complex permittivity increase with the increasing MWCNT concentration. We observe a percolation transition in the DC conductivity of the composites above a critical MWCNT concentration pc. The data from the twin-screw extruded samples give a very well-defined value of pc and a percolation exponent of 1.9 ± 0.2, in good agreement with theoretical predictions. In contrast, both the percolation threshold and the critical exponent were more poorly defined for the melt-mixed nanocomposites. This indicates that the conductive properties of these materials can strongly depend on the details of sample preparation. Our data suggest that the dc conductivity of the nanocomposites is due to the conduction along the nanotubes, coupled with thermally activated transport of electrons across thin polymer bridges, which separate the nanotubes. The frequency dependence of the dielectric spectrum was studied as a function of temperature and composition. The primary dielectric relaxation process is due to the motions of electric dipoles on the polymer backbone. At low MWCNT concentrations, the relaxation involves the entire polymer chains and is slowed substantially when a low concentration of MWCNT is added. At higher MWCNT concentrations, the relaxation becomes much faster. We attribute this to binding of the polymer chains to the nanotubes, which reduces the length of the chain segments contributing to the dielectric relaxation.