Given a wave duct with continuously variable parameters extending from y=0 to y=H, the reflection coefficients for originally plane downgoing and upgoing waves are written in the formR↓ = −exp(2iχ↓)andR↑ = minus;exp(2iχ↑), respectively. It is then shown that the characteristic equation governing the dispersion of undamped normal modes in the medium isχ↓+χ↑=mπ,mbeing an integer defining the mode number. χ↓ and χ↑ are solutions of nonlinear first‐order differential equations. If the medium consists ofnhomogeneous layers of finite thickness, the differential equation is replaced by a recursion relation, and the characteristic equation shown above includes one additional term.