Unusual single-pulse behaviour has been identified in two pulsars, B0919+06 and B1859+07. Both stars normally emit bright subpulses in a region near the trailing edge of their profile. However, they occasionally undergo 'events', whereby the emission longitude gradually decreases by about their profile width, remains in this position for typically several tens of pulses, and then gradually returns over a few pulses to the usual longitude. The effect bears some resemblance to a profile 'mode change', but here the effect is gradual and episodic. On close inspection, the separate profiles of the normal and 'event' in each pulsar emission reveal a broad and complex structure -but one which may be understood in terms of the geometry of a conical beam. Possibly the effect entails an extreme example of variable 'absorption' within the magnetosphere, as suspected in other pulsars. Alternatively, it may be caused by intrinsic changes in the emission within the pulsar's beam.