Typical block-oriented structure nonlinear systems include the basic input nonlinear systems,the output nonlinear systems,the input-output nonlinear systems and the feedback nonlinear systems.The input nonlinear systems include the input nonlinear equation-error type systems and the input nonlinear output-error type systems.Taking the input nonlinear equation-error autoregressive systems (namely the input nonlinear controlled autoregressive autoregressive (IN-CARAR) systems as an example,this paper studies and presents stochastic gradient (SG) identification methods,multi-innovation SG methods,recursive least squares (LS) identification methods and multi-innovation LS identification methods for IN-CARAR systems based on the over-parameterization model,the key term separation principle and the data filtering technique,the model decomposition technique.These methods can be extended to other input nonlinear equation-error systems,input nonlinear output-error type systems,output nonlinear equation-error type systems and output nonlinear output-error systems,and feedback nonlinear systems.Finally,the computational efficiency,the computational steps and the flowcharts of several typical identification algorithms are discussed.