Nonlinearity in the propagation and interaction of sound beams in real fluids is considered, with special emphasis on the effects of absorption. Asymptotic formulas are derived for the sum and difference frequency sound generated by two harmonic sound beams. The amplitude and phase conditions of the sources are arbitrary, within the limits imposed by the parabolic approximation. A distinction is made between two main contributions to the nonlinearly generated sound in the far field, the continuously pumped sound and the scattered sound. The relative amplitudes of the pumped and scattered waves are shown to depend critically on the frequency dependence of the absorption coefficients. Numerical results are presented for the noncollinear interaction of Gaussian primary beams, and also for second harmonic generation in the field of a circular uniform piston source.