For input nonlinear equation-error systems (namely the input nonlinear controlled autoregressive (IN-CAR) systems),this paper studies and presents the over-parameterization model based multi-innovation identification (MI) methods,the over-parameterization model based hierarchical MI methods and the key term separation based MI methods,and uses the decomposition technique to present the key term separation based two-stage MI methods and the key term separation based three-stage MI methods.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.