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As a consequence of the Maxwell equations, linear field gradients are accompanied by additional spatially dependent field components. A description of the Maxwell field terms is presented which explicitly takes into account the asymmetry of the gradient coil. It is shown both theoretically and experimentally that, in contrast to symmetric coils, an asymmetric coil generates concomitant field terms of zeroth and first order in space. Artifacts induced by concomitant fields can be much more pronounced for asymmetric coil designs than for symmetric ones. For the strong gradient amplitudes available on modern MR systems the effect of these concomitant magnetic fields on the evolution of magnetization has to be taken into consideration in a variety of NMR acquisition techniques. The formalism is used experimentally to compensate for artifacts observed in three different imaging methods: an image shift in standard echo planar imaging (EPI), an echo shift in diffusion-weighted EPI, and a phase shift in a flow quantification technique based on phase contrast images. Magn Reson Med 60:128–134, 2008. © 2008 Wiley-Liss, Inc.