The Landau-Vlasov initial-value problem is solved to second order in the field amplitude, using a secularity-free expansion method and neglecting no terms except of third and higher order. Apart from the Landau poles near the plasma frequency ωp, and the poles at the sum and difference frequencies near 2ωp and 0, also some new poles are found between 0 and ωp corresponding to second-order waves with the same phase velocity as one of generating first-order waves, and the difference of their wave numbers.