---

In this research, optimal design and assessment of multiple tuned mass dampers (MTMDs) capability in mitigating the damage of nonlinear steel structures subjected to earthquake excitation has been studied. Optimal parameters of TMDs on nonlinear multi-degree-of-freedom (MDOF) structures have been determined based on minimizing the maximum relative displacement (drift) of structure where for solving the optimization problem the genetic algorithm (GA) has been used successfully. For numerical analysis, three and nine storey 2-D moment resisting nonlinear steel frames subjected to far-field and near-field earthquakes and optimal MTMDs has been designed for different values of mass ratio and TMDs number. According to the results of numerical simulations, it can be said that MTMDs mechanism could reduce the damage of nonlinear steel structures where the effectiveness increases by increasing TMDs mass ratio. Also the performance of MTMDs depends on earthquake characteristics, mass ratio and TMDs configuration where in this research the effective case has been locating TMDs on top floor in parallel configuration.