A generalization of classical adiabatic molecular dynamics, which we term molecular dynamics with electronic frictions, is described for nuclear motion on a continuum of potential-energy surfaces, such as for adsorbate dynamics at a metal surface. In this situation, the Born-Opppenheimer approximation fails, since for any molecular motion-such as vibrations, rotations, or translations-there are resonant electronic excitations of the metal. However, such excitations are often highly delocalized, so that the continuum of electronic potential-energy surfaces on which nuclear motion occurs are all of similar shape, and can be replaced by a single, effective potential. Nonadiabatic energy exchange between nuclear and electronic degrees of freedom is then represented by frictional and fluctuating forces on the nuclei, and no explicit electronic dynamics are required. The friction in general involves memory, although it is shown that the Markov limit in which memory vanishes is likely to be quite broadly applicable. Expressions for the electronic friction in the Markov limit are obtained in terms of the electronic structure of the gas-surface system, which opens the way for direct calculation of these quantities. There is exact agreement between the frictions and previous time-dependent perturbation theory results fdr the lifetime of excited adsorbate vibrations at metal surfaces.