In order to help with the application of laser Doppler velocimetry to turbulent systems which include moving convoluted phase boundaries - e.g. turbulent flames - the interaction of the test beams with such interfaces is analysed. It is shown that there are two effects, one due to the changing phase difference, the other due to varying deflections, both of which cause the fringe grid to move in response to the velocity of the boundary. This is confirmed experimentally by recording an apparent velocity of a particle held stationary at the point of intersection of the two beams. The analysis indicates that the effect is serious only for near-tangential incidence to boundaries between hot and cold gas, when it tends to produce short bursts of large apparent velocities. Experimental methods of correction, or inactivation, of the system during such bursts of unreliability, are proposed.