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 ω_{p}, and the poles at the sum and difference frequencies near 2ω_{p} and 0, also some new poles are found between 0 and ω_{p} corresponding to second-order waves with the same phase velocity as one of generating first-order waves, and the difference of their wave numbers.