The relaxation processes of height undulations and density fluctuations in a membrane have been studied by molecular dynamics simulations of a coarse grained amphiphilic bilayer model. We observe a double exponential decay in their time correlations, with relaxation rates in good quantitative agreement with the theory by Seifert and Langer [Europhys. Lett. 23, 71 (1993)]. Intermonolayer friction due to slippage between the two monolayers is shown to be the dominant dissipative mechanism at the high wave numbers, q>10 µm−1, typically encountered in computer simulations. We briefly discuss the ramifications of the slow undulatory relaxation process for the calculation of bending rigidities from the static undulation structure factors. The relaxation rates are sensitive to the surface tension, and at high elongations an oscillatory contribution is observed in the time correlation of the undulations.