The main objective of this paper is to develop procedures to formulate sensitivity-state equations for systems with multi-terminal first-order linear components, whether active or passive, without using equivalent circuit techniques. Thereby, the sensitivity-state variables that appear are all directly measureable, with evident advantages when systems are being studied in the laboratory as well as simulated on the digital computer. The equations are obtained through a well-documented algorithm for picking the maximally selected formulation forest of the system graph under consideration. Using the concepts of state space it is seen that sensitivity functions may be obtained by calculating the responses of a dependent linear model, topologically equivalent to the original, with element values and driving functions determined by partial derivatives of the original system quantities. The process of automatic formulation and solution of the two classes of state models for the original and sensitivity systems is greatly facilitated because of the basic structural similarity among the two. The procedure can be extended to cover higher-order linear multi-terminal components, non-linear systems and higher-order sensitivity functions.