Nonlinear interaction of two collinear, spherically spreading sound beams is considered and applied to a discussion of parametric acoustic arrays. A general solution is given in the quasilinear approximation in terms of spherical harmonics and used to discuss the asymptotic behavior of the generated sound. Other expansions are also discussed. The main results, however, are obtained by introducing perturbation methods and deriving simplified equations governing the generated sound field, taking into account diffraction, absorption, and nonlinearity. From these equations, solutions are obtained and matched to give a solution valid in the whole space of propagation. Analytical and numerical results are presented and compared with available observations by different authors.