C-13 NMR spin-lattice relaxation time and nuclear Overhauser effect measurements are reported for linear polyethylene, polyethylene with long branches, and linear polyethylene with infrequent short branches at 75 MHz over the temperature range of 400-535 K. A quantitative description of the segmental dynamics of the main-chain methylene units and the branch points is obtained for linear polyethylene with ethyl branches. At 400 K, the correlation time is 29 ps for the segmental dynamics of the branch point but 5 ps for the segmental dynamics of the main-chain methylene units. The activation energy for the segmental dynamics of the main-chain methylene units (4 kcal/mol) is significantly less than the flow activation energy (E-eta = 7.2 kcal/mol). In contrast, the activation energy for the segmental dynamics at the branch point (6.4 kcal/mol) is much closer to E-eta. This result supports our earlier hypothesis that the lack of side groups in polyethylene allows conformational transitions to happen without substantial intermolecular cooperation. Thus, in contrast to many other polymers, conformational transitions are not the fundamental motion for flow in polyethylene. Branches as small as a methyl group introduce intermolecular cooperation into conformational transitions at the branch point, so conformational transitions at the branch points have a stronger temperature dependence. No difference in local dynamics was found for methylene units in linear polyethylene and polyethylene with long branches. Therefore, local dynamics are not relevant for understanding the factor-of-two difference in the flow activation energies of these two polymers.