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Attention is given to time-varying linear dynamic systems of a discrete or continuous time variable. For this class of systems the question of the existence and form of an inverse system is analyzed together with the question of decoupling a fixed plant by state variable feedback. It is shown that recent results (see , ) on the decoupling of stationary systems have a partial counterpart in the setting of nonstationary systems. A synopsis of the main results may be obtained by reading Theorem 1 and its corollaries.