For input nonlinear output-error systems with known bases,this paper presents the over-parameterization model based auxiliary model (AM) recursive identification methods,the over-parameterization model based AM hierarchical identification methods,the key term separation based AM recursive identification methods,the key term separation based AM two-stage recursive identification methods,the key term separation based AM three-stage recursive identification methods,the bilinear-in-parameter model decomposition based AM stochastic gradient identification methods and the bilinear-in-parameter model decomposition based AM recursive least squares identification methods.Finally,the computational efficiency and the computational steps of several typical identification algorithms are discussed.The convergence of the proposed algorithms needs further study.