The fast beta stress relaxation modes in a model polymeric melt are investigated by means of nonequilibrium. molecular dynamics simulations. The stress is computed on the atomic level by accounting for both bonded and nonbonded interatomic interactions. The system evolution is traced during the loading and relaxation periods, and the mechanisms of stress production are identified. Stress relaxation takes place by several modes, each corresponding to specific atomic-scale structural changes. The beta relaxation corresponds to the return to isotropy of the atomic distribution in the neighborhood of a representative atom and encompasses a quasielastic mode (beta1) and a slower mode (beta2). A diffusion-like process governs the beta2 mode. The beta1 mode is nonexponential and accounts for roughly 50% of the total atomic-scale stress drop during relaxation. The beta2 mode is exponential and leads to a smaller stress drop, but it takes longer to complete than beta1. Both beta modes involve only local structural changes, and their time constants are independent of the molecular weight of the chains. These are simple thermally activated processes that do not involve cooperative relaxations and whose temperature dependence can be described by an Arrhenius equation. Furthermore, it is shown that the time constant for the exponential mode, beta2, can be derived from equilibrium simulations based on the fluctuation-dissipation theorem and a continuum model of diffusion in the neighborhood of a representative atom. This shows that the nonequilibrium system is in the linear-response regime during this relaxation stage.