The behaviour of S.O.R. iterations for linear equations AU = Bis described for the case when A is singular. Small inconsistencies may arise in practical application, for example in systems derived from Neumann problems. In that case the S.O.R. iterations do not converge. A simple transformation is presented under which the iterations converge to an approximate solution of AU = B, provided that the singularity of A is of a simple type. A practical way of measuring the appropriate convergence rate is also described. For problems with property (A) and consistent ordering the optimum acceleration parameter is unaffected by the simple singularity of A. The behaviour of the iterations when A has singularities of general type is also described.