The auxiliary model identification idea,the multi-innovation identification theory and the coupling identification concept are the new ideas and principles for studying identification problems of complex systems.Combining them,this paper studies the identification methods of multivariable output-error-like systems and presents multivariate auxiliary model identification methods,multivariate auxiliary model based multi-innovation identification methods,interval-varying multivariate auxiliary model based multi-innovation identification methods.In order to reduce the computational complexity of the algorithms,we decompose the system into several sub-identification models and derive the partially coupled auxiliary model based identification methods and the partially coupled auxiliary model based multi-innovation identification methods,using the auxiliary model identification idea,the multi-innovation identification theory and the coupling identification concept.Finally,the computational efficiency,the computational steps and the flowcharts of some typical identification algorithms are discussed.