Asymmetrical buildings on application of lateral loads are observed to be résponding differently compared to symmetric building and the edge frames act as flexible or stiff based on the direction of eccentricity. Variations of the responses of the asymmetrical building at flexible edge and stiff edge are quantified in terms of peak displacements, drifts, shears and accelerations at different stories. In this paper, responses of a typical ten storey reinforced concrete (RC) asymmetrical building with and without passive energy dissipators are studied for four different earthquake ground motions. In the present study, different eccentricity ratios are considered by varying eccentricities in X direction of the building to be 0% to 30% and lateral loads are assumed to be acting in the Y-direction of the building. To bring down the peak seismic responses of the asymmetric building, applicability of designing two different passive dampers viz. Viscoelastic dampers (VED) and Tuned mass damper (TMD) are explored. Sensitivity of response ratio of peak displacements at roof level and ratio of peak base shear with and without VED and TMD are studied for different eccentricity ratios and torsional to translational frequency ratios. From the studies, the necessity to include the effect of asymmetry of the building in the design of VED and TMD are brought out.