AbstractThe aim of the research reported in this paper is to extend the notion of invariant sensitivity sum, widely known for electrical networks, from first‐order sensitivities to high‐order sensitivities. The results are high‐order invariant sums of sensitivities of the first and the second kind, formulated for nonlinear lumped circuit, which consists of one‐port and two‐ports only. One‐ports are generalized resistances, capacitances, inductances, voltages, and current sources, whereas two‐ports are nonlinear generalizations of four types of controlled sources. It is observed that the invariant sums actually found for nonlinear lumped networks are generalizations of sums given earlier by authors for linear lumped networks. The article is illustrated by numerical sensitivity analysis of simple linear and nonlinear circuits. Copyright © 2010 John Wiley & Sons, Ltd.