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Following the general approach called "composite system method," the analysis of the stability of large-scale systems is carried out on the basis of a simplified input-output description of each subsystem. Two different cases are considered and investigated. The a priori knowledge is assumed to be for the first case a simplified input-output description of each subsystem, and for the second case a simplified description of the internal structure. The resulting stability criterion is also applicable to subsystems with unstable uncertainties and, therefore, provides an extension of the applicability limits of already known procedures.