This paper deals with the analysis of nonlinear circuits that interconnect passive elements (capacitors, inductors, and resistors) with nonlinear resistors exhibiting a range of negative resistance. Active elements are necessary to design physical circuits that switch and oscillate. We generalize the classical passivity theory of circuit analysis to develop a port interconnection theory for such non-equilibrium behaviors. The approach closely mimics the classical methodology of (incremental) dissipativity theory, but with dissipation inequalities that combine signed storage functions and signed supply rates to account for the port interconnection of passive and active elements.