The decay of fluctuations in fluid biomembranes is strongly stretched and nonexponential on nanometer lengthscales. We report on calculations of structural correlation functions for lipid bilayer membranes from atomistic and coarse-grained molecular dynamics simulations. The time scales extend up to microseconds, whereas the linear size of the largest systems is around 50 nm. Thus, we can cover the equilibrium dynamics of wave vectors over two orders of magnitude (0.2-20 nm(-1)). The time correlations observed in the simulations are best described by stretched exponential functions, with exponents of 0.45 for the atomistic and 0.60 for the coarse-grained model. Area number density fluctuations, thickness fluctuations, and undulations behave dynamically in a similar way and have almost exactly the same dynamics for wavelengths below 3 nm, indicating that in this regime undulations and thickness fluctuations are governed by in-plane density fluctuations. The out-of-plane height fluctuations are apparent only at the longest wavelengths accessible in the simulations (above 6 nm). The effective correlation times of the stretched exponentials vary strongly with the wave vector. The variation fits inverse power-laws that change with wavelength. The exponent is 3 for wavelengths smaller than about 1.25 nm and switches to 1 above this. There are indications for a switch to still another exponent, 2, for wavelengths above 20 nm. Compared to neutron spin-echo (NSE) experiments, the simulation data indicate a faster relaxation in the hydrodynamic limit, although an extrapolation of NSE data, as well as inelastic neutron scattering data, is in agreement with our data at larger wave vectors.