Abstract—Viscous Dampers (VDs) are widely used as passive energy dissipation system for improving seismic performance levels especially in retrofitting of buildings. Residual Inter-story Drift Ratio (R-IDR) is another important factor that specifies the condition of building after earthquake. The values of R-IDR illustrates the possibility of retrofitting and repairing of a building. Therefore, this study aims to explore the vector-valued Intensity Measures (IMs) for predicting the R-IDR of two group of steel Moment-Resisting Frames (MRFs) with and without implementing VDs. Incremental Dynamic Analysis (IDA) was performed with considering RIDR using OpenSees software. Efficiency and sufficiency have been quantified for 18 vector-valued IMs with respect to the Residual Interstory Drift Ratio (R-IDR). Results showed that two vector-valued IMs of (Sa(T1), SaRatioM-D) and (Sa(T1), IM-D) had lower σlnSaRD|IM2 values in the R-IDR of 0.002, 0.005, 0.01, and 0.02, and they had higher FR in the mean dispersion, (σlnSaRD|IM2)avg, compared to other IMs. In addition, two vector-valued IMs of (Sa(T1), SaRatioM-D) and (Sa(T1), IM-D) achieved p-values higher than 0.05 with respect to seismic ground motion features of M, R, and Vs30, and can be used as optimal vector-valued IMs.