Wavelet transforms provide a valuable new tool for analysis of tidal processes that deviate markedly from an assumption of exact periodicity inherent in traditional harmonic analysis. A wavelet basis adapted to nonstationary tidal problems is constructed and employed to analyze the modulation of the external tide in a river by variations in streamflow. Interaction of a surface tide with river flow is the best available demonstration of the continuous wavelet transform (CWT) methods developed. It is the simplest and perhaps the only nonstationary tidal process for which both sufficient data and dynamical understanding exist to allow detailed comparisons between CWT analyses and analytical predictions of the response of tides to nontidal forcing. Variations at up-river locations of low-frequency elevation (river stage ZR) and three tidal species are deduced from cross-sectionally integrated equations. For landward propagation in a channel of constant cross section with quadratic friction, the log of the amplitude of the diurnal (D1), semidiurnal (D2) and quarterdiurnal (D4) elevations should vary at far upriver locations with the square root of the river flow (QR), and river stage (ZR) should depend on the square of river flow. Convergent geometry and species-species frictional interactions modify these predictions somewhat. CWT analyses show that the predicted amplitude behavior for the tidal species is approximately correct. Best results are obtained for the dominant, dynamically simplest processes (ZR and D2). In the past, further progress in understanding river tides has been limited by a lack of data analysis tools. Data analysis tools are now clearly better than the available analytical solutions.¿ 1997 American Geophysical Union