In this paper we discuss the wave-wave coupling of two high-frequency electromagnetic waves launched into a warm plasma across the constant confining magnetic field using the Maxwell-Vlasov equations for electrons. Specifically, we consider the generation of an ordinary wave by the interaction of an extraordinary and an ordinary wave and the generation of an extraordinary wave by the interaction of two ordinary ones. The decay conditions and the amplitudes of the secondary waves are discussed numerically for different values of the electron temperature.