The input nonlinear systems include the input nonlinear equation-error type systems and the input nonlinear output-error type systems.According to the over-parameterization model,the key term separation and the data filtering,this paper studies and presents the over-parameterization model based auxiliary model recursive identification (AM-RI) methods,the key term separation based AM-RI methods and the data filtering based AM-RI methods for input nonlinear output-error autoregressive systems.These methods can be extended to other input nonlinear output-error systems,output nonlinear output-error type systems and feedback nonlinear systems.Finally,the computational efficiency,the computational steps and the flowcharts of several typical identification algorithms are discussed.