In order to evaluate the dynamic behavior of passive energy dissipation system, two steps need to be considered for prediction of structural response in the presence of ductile element in an off-centre bracing system. The first is a detailed analysis of the proposed ductile element and the second is the effect of this ductile element on an off-centre bracing system. The use of ductile bracing system is expanding in steel structures in order to increase the force reduction factor. Therefore, regarding the nonlinear behavior of steel material used in an off-centre bracing systems and using ductile element in OBS bracing systems, the seismic evaluation of the mentioned systems seems to be necessary. This paper aims to study linear and nonlinear behavior of steel frames with off-centre bracing system and ductile element, in order to get the best position of these bracing elements. To achieve this purpose, the modeling has been done with ANSYS software. The optimum eccentricity has been obtained by modeling three steel frames with different eccentricities and evaluating the results of them. The analytical results showed that the model OBS-C with 0.3 eccentricities has higher performance among the models.