The Krylov‐Bogoliubov‐Mitropolsky perturbation method is applied to systems of nonlinear dispersive waves including plasma waves such as ion‐acoustic, magneto‐acoustic, and electron plasma waves. It is found that long time slow modulation of the complex wave amplitude can be described by the nonlinear Schro¨dinger equation for a very wide class of nonlinear dispersive waves.