According to the hierarchical identification principle,this paper presents the hierarchical stochastic gradient algorithms and the hierarchical gradient based iterative algorithms,the hierarchical least squares algorithms and the hierarchical least squares based iterative algorithms for multivariable equation-error-like systems and multivariable equation-error ARMA-like systems,and further derives the hierarchical multi-innovation gradient algorithms and the hierarchical multi-innovation least squares algorithms.In order to reduce computational burdens,this paper derives the filtering based hierarchical identification algorithms and the filtering based hierarchical multi-innovation identification algorithms for multivariable equation-error ARMA-like systems using the filtering technique. Finally,the computational efficiency and the computational steps of some typical identification algorithms are discussed.