Abstract This paper presents a stability criterion for a class of nonlinear RLC networks for which the nonlinear characteristic curves lie in Popov sectors. The nonlinear elements considered are resistors, charge-controlled capacitors, and flux-controlled inductors. It is shown that if the only nonlinear elements are resistors, then for arbitrarily large sector boundaries the circuit is both asymptotically stable in the large and, for properly placed sources, bounded-input bounded-output stable. Furthermore, if the only nonlinear elements are inductors and capacitors, any set of linear inductors and capacitors which can make the circuit oscillate define the nonlinear sector boundaries. Conditions for asymptotic stability and bounded-input bounded-output stability for networks of nonlinear resistors, inductors, and capacitors are developed.