A new high-frequency asymptotic theory of propagation in ducts with a continuously varying refractive index is presented. The theory is based on local wave fields with complex phase and constitutes a special application of the evanescent wave tracking theory. It is shown, for analytic profiles and for refractive indexes that vary only transversely to the duct direction, how the coefficients in the asymptotic expansion are evaluated explicitly. When the method is applied to parabolic and hyperbolic secant profiles for which exact solutions of the wave equation are available, the asymptotic expansions so generated agree term by term with the asymptotically expanded exact results. The method is then applied to a class of polynomial profiles for which exact results in terms of known functions are not available.