The method of expansion in instantaneous eigenfunctions is used to obtain approximate solutions to the linearized Vlasov equation when the unperturbed function is time‐dependent. The method is useful when the time‐dependence of the unperturbed function is slow compared with the plasma frequency. The general results are used to obtain the growth of wave energies in the quasilinear limitation of weak two‐stream instabilities. Deviations from previous results for this problem are found.