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The potential of post-tensioned self-centering moment-resisting frames (SC-MRFs) and viscous dampers to reduce the economic seismic losses in steel buildings is evaluated. The evaluation is based on a prototype steel building designed using four different seismic-resistant frames: (i) conventional moment resisting frames (MRFs); (ii) MRFs with viscous dampers; (iii) SC-MRFs; or (iv) SC-MRFs with viscous dampers. All frames are designed according to Eurocode 8 and have the same column/beam cross sections and similar periods of vibration. Viscous dampers are designed to reduce the peak story drift under the design basis earthquake (DBE) from 1.8% to 1.2%. Losses are estimated by developing vulnerability functions according to the FEMA P-58 methodology, which considers uncertainties in earthquake ground motion, structural response, and repair costs. Both the probability of collapse and the probability of demolition because of excessive residual story drifts are taken into account. Incremental dynamic analyses are conducted using models capable to simulate all limit states up to collapse. A parametric study on the effect of the residual story drift threshold beyond which is less expensive to rebuild a structure than to repair is also conducted. It is shown that viscous dampers are more effective than post-tensioning for seismic intensities equal or lower than the maximum considered earthquake (MCE). Post-tensioning is effective in reducing repair costs only for seismic intensities higher than the DBE. The paper also highlights the effectiveness of combining post-tensioning and supplemental viscous damping by showing that the SC-MRF with viscous dampers achieves significant repair cost reductions compared to the conventional MRF