The method of Eshelby et al. transforms the non-linear equations of equilibrium of a group of dislocations, free to move in one dimension in a stress field, into another set of non-linear equations, greater in number but of a simpler form. The examples considered by Eshelby et al. are special cases for which the transformed equations are linear. The complexity of the transformed equations is shown to depend on the form of the stress field. The method is extended to dislocations which may be of opposite signs and which are free to move in two dimensions.