The application of singular perturbation techniques to problems in nonlinear acoustics is demonstrated in two examples. In the first, we show that straightforward perturbation methods, using Lighthill's equation for aerodynamic sound, give a secular series when applied to one-dimensional simple wave flow. The nonuniform secular terms are removed by the introduction of expansions in terms of multiple scaled coordinates, and the Earnshaw solution for the shock-free region is recovered. Such an expansion technique is also applied to solve a problem in compound flow. In the second example, the method of matched asymptotic expansions (MAE) is applied to one-dimensional flow governed by Burgers' equation. If the excitation at the origin is time harmonic, Burgers' equation can be solved exactly, and the solution reduced to an intelligible form in the shock-free, saw-tooth, and saturation regions. These simplified approximate solutions are recovered by a direct application of MAE to Burgers' equation, and in work still under completion, it appears that the same process will yield a uniformly valid approximate solution of the analogous problems in two and three dimensions.