The self-diffusion coefficient, D, and zero-shear rate viscosity, eta, were measured in the melt state for a series of nearly monodisperse model polyethylenes ranging in molecular weight from 10(3) to 10(6). The samples were prepared by hydrogenating anionically polymerized polybutadienes and contain similar to 2 ethyl branches/100 CH2 units. The results were compared with molecular theory, both as the product eta D, whose value is independent of the monomeric friction factor, and as individual values of eta and D after correcting to a constant friction factor. At low molecular weights eta D and the corrected eta and D separately agree very well with predictions based on the Rouse model. At higher molecular weights, where chain entanglement becomes important, the data clearly show that relaxation mechanisms beyond those considered in the Doi-Edwards tube model make significant contributions to both self-diffusion and viscosity. Comparisons with data for polystyrene and hydrogenated polyisoprene suggest that these departures are universal.