We expand the compressible magnetohydrodynamic (MHD) equations in terms of the amplitude of first-order Alfv¿n waves. Incompressible MHD equations are treated as a special case. We examine the evolution of mildly oblique Alfv¿n waves consisting of forward and backward propagating waves so that these would correspond to the interactions of outgoing and ingoing Alfv¿n waves in the solar wind. We obtain the solutions of these equations through second order. We find and distinguish three types of second-order modes which have zero frequency and are generated in association with nonsecular interactions of mildly oblique first-order Alfv¿n waves. Two of these modes have wave vectors which are perpendicular to the background magnetic field. Both are associated with magnetic energy but they do not have kinetic energy.