The propagation and scattering of waves in nonuniform flows is modeled using the Euler equations linearized about a nonuniform mean flow. The formulation requires inflow/outflow conditions to complete the initial or boundary-value problem. For a nonuniform flow in a duct, the usual splitting between acoustic, entropic and rotational waves is not possible, and the normal mode analysis shows, in general, discrete and continuous spectra. The modes are segregated using the Bers-Briggs criteria, which for stable modes show that the group velocity gives the direction of propagation. Exact nonreflecting conditions can then be derived. The accuracy will be demonstrated with examples of acoustic and vorticity waves propagating in a duct.