For multivariate pseudo-linear regressive moving average systems,a multivariate extended stochastic gradient(ESG) algorithm is discussed.In order to reduce the computational cost of the identification algorithm,we decompose a multivariate system into several subsystems,and derive a partially coupled(subsystem) ESG algorithm and a partially coupled(subsystem) multi-innovation ESG algorithm according to the coupling identification concept and the multi-innovation identification theory.Furthermore,we extend these methods to multivariate pseudo-linear autoregressive moving average systems and present a partially coupled(subsystem) generalized extended stochastic gradient(GESG) algorithm and a partially coupled(subsystem) multi-innovation GESG algorithm.The computational efficiencies of the multivariate ESG algorithm,the partially coupled ESG algorithm and the partially coupled multi-innovation ESG algorithm are analyzed.