The problem of obtaining a reduced-order model is considered for an interconnected high-order system which is composed of several subsystems. For such systems, retaining the internal structure of the original system in a reduced-order model is quite important from an engineering point of view. Of course the most desirable solution to the problem would be to derive an algorithm for constructing a reduced-order model under a single criterion, but unfortunately such an approach has not been found yet. Instead, we proceed to approximate each subsystem by reduced-order models and combine the results. In this case the following questions arise. (a) Does the reduced-order model obtained as above preserve the stability property under the assumption that the original system is stable? If not always, under what conditions? (b) How does the reduced-order model approximate the input-output characteristics of the original system? The present work answers these questions and the validity of the proposed method is pointed out via a numerical simulation.