In the present work, we report on a systematic analysis to determine the maximum time step allowed in molecular dynamics simulations applied to study metal systems of current interest in nanoscience. Using the velocity Verlet integration scheme, we have found that it is possible to use a 20 fs time step for the simulation of gold nanosystems. This is roughly an order of magnitude greater than the usually employed integration step (2 to 5 fs). We also propose a general criterion to select this maximum time step for other metallic nanosystems, even in the case of bimetallic nanosystems.