This paper proposes a feedback structure for the design of l2-stable algorithms for nonlinear adaptive filtering and identification, and establishes explicit connections between classical schemes in IIR modeling and more recent results in H∞ theory. In particular, two algorithms due to Feintuch and to Landau, as well as the so-called pseudo-linear regression and Gauss-Newton algorithms, are discussed within the framework proposed here. Additional examples and simulation results are included to illustrate the applicability of the approach to several nonlinear scenarios.