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The invertibility, reproducibility and decoupling of the class of systems of the Hammerstein form is studied. The criteria for invertibility and reproducibility are given in terms of those of the linear dynamic subsystem and in terms of the memoryless nonlinearity in the feedforward path (independently of feedback). It is shown that such a system can be decoupled by dynamic precompensation and (nonlinear) state feedback if and only if it is invertible. For static (no dynamics) decoupling, and additional requirement, namely, the static (G,F)-decouplability of the linear dynamic subsystem, is needed.