The paper introduces the concept of Kirchhoff interconnection, proper to multi-variable dynamical systems, and characterized by relations which generalize in a certain sense those relations as set down by Kirchhoff's theorems for an electric network with one independent node and an arbitrary number of independent loopa. It also defines the partially reversing system, the conditions of Kirchhoff interconnectability, and some aspects of the output controllability and input observability of Kirchhoff interconnectable and interconnected systems.