The optical parametric oscillator and amplifier involving the analogue of the inverse Cerenkov effect is considered, the effect being due to the non-linear interaction between the plane wave of pumping (with a frequency yp) incident at an angle onto an optical waveguide and the waves (with frequencies ys, yvsatisfying the relation ys+ yv= yp) generated in the waveguide. For the oscillator an appreciable non-linear reflection from (transmission through) the waveguide layer of the pumping wave is discovered and shown to appear in new directions compared to those known in optics. Also, the transformation by the reflection (transmission) of the pumping wave into the waves with new frequencies 2 ys, 2yvis predicted. The possible effect of additional (higher-order) non-linear processes on the oscillator dynamics is discussed. A travelling-wave parametric amplifier involving the analogue of the inverse Cerenkov effect is also considered. Here, differing from the usual optical parametric amplifiers the intensities of generated waves (limited by the non-linear Cerenkov losses) are shown to exceed appreciably the intensity of the incident pumping wave. Possible difference and sum-frequency generation involving the analogue of the inverse Cerenkov effect in a waveguide is noted as well.