Let S be a system resulting from the interconnection of several subsystems, identified through their corresponding input and output channels. The problem studied is to find the conditions for local output feedbacks to exist such that the resulting closed-loop system is controllable and observable from a single channel. For the case of two interconnected systems the above problem is solved by the methods of system theory in the operator (frequency) domain, based on polynomial matrices. An extension of these results and the use of graph theoretic methods also give a solution to the general case. The problems when local dynamic feedbacks and local state feedbacks are considered are also sketched, and it is shown how they fit into the present context.