This paper initiates the derivation of a general analytical model for nonlinear effects in sound beams driven at high source pressure levels. The excitation is generated by a planar transducer that is in harmonic motion in an arbitrary axisymmetric pattern. The analysis develops a perturbation solution of a nonlinear equation for the velocity potential. The first‐order term, which is derived with the aid of a Hankel transform to represent the transverse dependence, is the King integral for a linear sound beam. Using this integral to form the source terms exciting the second‐order potential leads to a dual Hankel transform. Reduction to a single integral is achieved with the aid of an asymptotic integration following Laplace’s method. The second‐order term that is derived in this manner describes the tendency for the second harmonic to grow with increasing distance from the source. This result is an intermediate step in the overall development, because the integrand loses validity in the spectrum of transverse wavenumbers near the transition between evanescent and propagating wavelets, as well as for increasing distance from the transducer.