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In close binary stars, the tidal excitation of pulsations typically dissipates energy, causing the system to evolve towards a circular orbit with aligned and synchronized stellar spins. However, for stars with self-excited pulsations, we demonstrate that tidal interaction with unstable pulsation modes can transfer energy in the opposite direction, forcing the spins of the stars away from synchronicity, and potentially pumping the eccentricity and spin-orbit misalignment angle. This "inverse" tidal process only occurs when the tidally forced mode amplitude is comparable to the mode's saturation amplitude, and it is thus most likely to occur in main sequence gravity mode pulsators with orbital periods of a few days. We examine the long-term evolution of inverse tidal action, finding the stellar rotation rate can potentially be driven to a very large or very small value, while maintaining a large spin-orbit misalignment angle. Several recent asteroseismic analyses of pulsating stars in close binaries have revealed extremely slow core rotation periods, which we attribute to the action of inverse tides.