This paper deals with recursive parameters estimation of nonlinear systems in the presence of unknown but bounded disturbances. The proposed technique is performed by the use of a modified extended least squares algorithm so that the estimated parameters are consistent with the measurements and the noise constraints while local asymptotic convergence, under very general conditions, is assured. One of the main features is to show, from the stability analysis, connection between some arbitrary factors and basin of attraction. High performances, from the design and implementation point of view, will be shown through a numerical example under severe conditions.