An analysis of acoustic wave propagation in a waveguide carrying an incompressible mean flow is presented. The radius of the waveguide is taken to vary slowly as a function of axial location. It is shown that the dynamic behavior of the enclosed fluid can be parametrized by the small parameter where is the ratio of the typical duct radius R 0 and the wall wavelength L 0. An analytical solution for the pressure field in the duct is given in terms of a regular perturbation expansion in The method of matched asymptotic expansions is used to evaluate the refractive effect of a thin mean-flow boundary layer on the acoustic pressure field. It is shown that in the case where the duct geometry conforms to that of a circular cosh duct the effect of higher-order turning points in the wave equation can be effectively handled by a closed-form solution that approximately solves the governing equations. The results of analysis are compared to those obtained using numerical methods. 1987 Acoustical Society of America