We have previously reported on a complex-difference (CD) flow measurement technique that produces more accurate results than the phase-difference (PD) flow measurement technique due to the greater immunity of the former method to partial volume effects. We report here on some of the ways in which through-plane myocardial motion affects the accuracy of absolute coronary artery flow measurements obtained using the PD and CD techniques. We also discuss motion correction schemes that can be applied to the PD and CD processing methods to improve their accuracy. Computer simulations have been performed to assess the magnitude of the errors associated with these flow measurement techniques when they are applied to small vessels that are attached to a moving background. Laminar and plug flow, with and without complete background suppression, have been considered. Experiments with a moving vessel phantom have been conducted to test the performance of the PD and CD flow measurement techniques in circumstances similar to those simulated. The simulations and the experiments showed that, after corrections for through-plane motion are made, the CD method generally yields more accurate flow results than the PD method. As shown by the simulations, however, both methods yield compromised results due to subtle saturation effects that occur when the direction of myocardial motion is opposite the direction of blood flow. Unvalidated PD and CD measurements of coronary artery flow waveforms in human volunteers are presented to illustrate the magnitude of the proposed through-plane motion effects in vivo.