Even simple circuits containing only one op amp and linear resistors can have multiple d.c. operating points. Using a realistic non-linear d.c. op-amp model which includes the saturation characteristics, this paper gives the necessary and sufficient conditions for an arbitrary op-amp circuit (containing op amps, linear resistors, strictly-increasing non-linear resistors and independent sources) to have a unique solution for all values of circuit parameters. These conditions are remarkable because they are couched strictly in topological terms. For many op-amp circuits (e.g. those containing only one op amp), the necessary and sufficient conditions can be checked by inspection.