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This paper researches the identification problem for the unknown parameters of the multivariate equation-error autoregressive systems. Firstly, the original identification model is decomposed into several sub-identification models according to the number of system outputs. Then, based on the characteristic that the information vector and the parameter vector are common among the sub-identification models, the coupling identification concept is used to propose a partially coupled generalized stochastic gradient algorithm. Furthermore, by expanding the scalar innovation of each subsystem model to the innovation vector, a partially coupled multi-innovation generalized stochastic gradient algorithm is proposed. Finally, the numerical simulations indicate that the proposed algorithms are effective and have good parameter estimation performances.