We provide a time-domain robustness analysis of Gauss-Newton recursive methods that are often employed in identification and control. Several free parameters are included in the filter description while combining the covariance update and the weight-vector update, with the exponentially weighted recursive-least-squares (RLS) algorithm being an important special case. One of the contributions of this work is to show that by properly selecting the free parameters, the resulting filter can be made to impose certain bounds on the error quantities, thus resulting in desirable robustness properties (cf. H 1 -theory). We also show that an intrinsic feedback structure, mapping the noise sequence and the initial weight error to the apriori estimation errors and the final weight error, can be associated with such recursive schemes.