The interaction of geostrophic zonal mean currents in an equatorial ocean with free, neutrally stable, internal Kelvin and inertio-gravity waves is investigated using a two-layer, reduced-gravity model. Solutions in the inertio-gravity range are obtained by a simple numerical integration scheme that allows several different background flows to be tested. It is found that, due to the interaction, the amplitudes and latitudinal distributions of wave zonal velocity are substantially altered from those which would occur in the absence of mean flow. Meanders of currents similar to those observed during GATE may be interpreted as advections of mean currents by wave meridional velocity. On the other hand, wave pressure (sea level) and meridional velocities are not greatly affected by the mean flow. These results may be of importance in attempting to fit equatorial wave theories to observations of zonal current, on the one hand, and of sea level fluctuations on the other. Kelvin waves are treated using a perturbation expansion based on the small ratio of mean current speed to wave phase speed. The shear flow alters low-frequency Kelvin waves only slightly, introducing a small meridional velocity and a Doppler shift which could affect the speed of baroclinic adjustments in the tropics. At higher frequencies, the Kelvin wave becomes more like an inertio-gravity wave and may appear in velocity records as varicose meanders of the background current.