In today's world of signal processing, nonlinear systems have been attained a considerable importance in the field of system identification and system control. The modeling of many physical systems was introduced by a nonlinear Wiener model consists of static nonlinear function followed by a linear time invariant (LTI) dynamic system. The output of the nonlinear function is considered to be continuous and invertible. This work leads the identification of Wiener model parameters using least mean square (LMS) algorithm and its two different variants named leaky LMS and modified leaky LMS due to its simple and effective adaptive nature. The simulation results for an example supporting the deduced methodology are obtained to effectively analyze the algorithm performance. © 2017 IEEE.