Abstract By combining a high sensitive dielectric sensor into a parallel plate rheometer, the time evolution of the dielectric properties of polyethylene/carbon nanotube composites was measured in the molten state under oscillatory shear. Composites with single- (SWCNT) or multiwall (MWCNT) carbon nanotubes initially decrease its conductivity proportional to the oscillatory shear-strain applied. After this initial drop, some composites increase the conductivity under these non-quiescent conditions reflecting a possible shear-induced agglomeration process. The latter based on the complex permittivity spectrum showing a shortening in the CNT–CNT distances in these composites after shear. At concentrations below the electrical percolation threshold, the presence of both SWCNTs and MWCNTs reduces the DC conductivity of the molten matrices. This result shows that carbon nanotubes can act as a scavenger for impurities or additives present in commercial polyethylenes.