Since long time coil corifigurations of high order have been well known and often used to produce magnetic fields of high quality for axially symmetric homogeneous and gradient coils. However, the transversal gradients which are equally necessary for Magnetic Resonance Imaging (MRI) are less explored. We present a family of solutions which need a minimum amount of Simple geometrical elements, the most sophisticated having field error contributions of order 9 and higher. © 1990, IEEE. All rights reserved.