This paper presents a generalization of the chain-scattering representation to the case of general plants. Through the notion of input-output consistency, the conditions under which the generalized chain-scattering representation (GCSR) and the dual-generalized chain-scattering representation (DGCSR) exist are proposed. The generalized chain-scattering matrices are formulated into a general parameterized form by using the generalized inverse of matrices, Some algebraic system properties, such as the cascade structure property, the symmetry (duality) of the GCSR＇s and DGCSR＇s, are studied.