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The inhomogeneity of the main magnetic field is a significant factor limiting the performance and increasing the cost of commercial magnetic resonance imaging (MRI) and spectroscopy machines. This is particularly true where shielding is employed to limit fringing fields. In this paper, we investigate the performance of a recently introduced MRI technique using time-varying gradients in the presence of such inhomogeneity. It is shown that the time-varying gradient imaging system can accommodate considerable inhomogeneities (1000 ppm in typical imaging application). The problem of selection of the gradient frequencies for simultaneous multiple dimension imaging in the presence of inhomogeneity is formulated and solved.