This study investigates the effect of nonlinear inertia on the dynamic response of an asymmetric building equipped with Tuned Mass Dampers (TMDs).In the field of structural engineering,many researchers have developed models to study the behavior of nonlinear TMDs,but the effect of nonlinear inertia has not received as much attention for asymmetric buildings.To consider nonlinear inertia,the equations of motion are derived in a local rotary coordinates system.The displacements and rotations of the modeled building and TMDs are defined by five-degree-of-freedom (5-DOFs).The equations of motion are derived by using the Lagrangian method.Also in the proposed nonlinear model,the equations of motion are different from a conventional linear model.In order to compare the response of the proposed nonlinear model and a conventional linear model,numerical examples are presented and the response of the modeled buildings are derived under harmonic and earthquake excitations.It is shown that if the nonlinear inertia is considered,the response of the modeled structures changes and the conventional linear approach cannot adequately model the dynamic behavior of the asymmetric buildings which are equipped with TMDs.