For multivariable equation error moving average systems,this paper gives an extended stochastic gradient identification algorithm,a recursive extended least squares identification algorithm,a gradient based iterative(GI) identification algorithm and a least squares based iterative(LSI) identification algorithm,using the least squares principle and the iterative search principle.For multivariable equation error moving average systems and multivariable equation error autoregressive moving average systems,this paper uses the coupling identification concept and decomposes a multivariable system into several subsystems,derives the corresponding GI identification algorithm,partially coupled(subsystem) GI identification algorithm,subsystem LSI identification algorithm and partially coupled subsystem LSI identification algorithm.Furthermore,using the filtering technique,this paper studies the subsystem GI identification algorithm,partially coupled (subsystem) GI identification algorithm,partially coupled subsystem LSI identification algorithm for multivariable equation error autoregressive moving average systems.The computational steps for several typical identification algorithms are provided.