The dynamical characteristics of ring and linear polyethylene (PE) molecules in the melt have been studied by employing atomistic molecular dynamics simulations for linear PEs with carbon atom numbers N up to 500 and rings with N up to 1500. The single-chain dynamic structure factors S(q,t) from entangled linear PE melt chains, which show strong deviations from the Rouse predictions, exhibit quantitative agreement with experimental results. Ring PE melt chains also show a transition from the Rouse-type to entangled dynamics, as indicated by the characteristics of S(q,1) and mean-square monomer displacements g(1)(t). For entangled ring PE melts, we observe g(1)(t) similar to t(0.35) and the chain-length dependence of diffusion coefficients D-N proportional to N-1.9, very similar to entangled linear chains. Moreover, the diffusion coefficients D-N remain larger for the entangled rings than the corresponding entangled linear chains, due to about a 3-fold larger chain length for entanglement. Since rings reptate, our results point toward other important dynamical modes, based on mutual relaxations of neighboring chains, for entangled polymers in general. do not