The phase-encoded method of NMR flow imaging is examined in detail. The motion of isochromatic groups in the direction of suitably balanced magnetic field gradients will give a phase change in the NMR signal directly proportional to the velocity, acceleration, or higher derivative of position, dependent upon the form of the field gradient. If a simple bipolar pulse is used then the phase change, for isochromats moving with constant velocity, will be proportional to the velocity. If two such pulses are placed back to back then the phase change is proportional to the acceleration. The motion of isochromats in the magnetic field gradients used for imaging will also cause phase changes. These effects are considered, and simple methods of reducing them presented. Phase errors due to main field inhomogeneity are shown to be eliminated by a simple phase difference technique. In this two image data sets having different flow sensitivities are obtained, and the phase difference between them calculated. Velocity images were obtained using this technique, both by the manipulation of the frequency-encoding and selection gradients, and by the insertion of bipolar pulses in the imaging sequence. Acceleration images were also produced by adding double bipolar pulses to the imaging sequence. Both spin-echo and field-echo sequences were used. Field-echo sequences were shown to be superior for high velocities, particularly when the direction of flow is through the slice, otherwise spin-echo sequences were preferred. The Fourier imaging of velocity is also examined, and images presented. This technique is only considered to be useful for projective imaging, where it is shown to have an SNR advantage over established methods. Using two specially designed phantoms the accuracy of all these techniques is shown to be within 5%.