This study investigates the effects of ground-motion sequences on fragility and vulnerability of reinforced concrete (RC) moment-resisting frames (MRFs). Two four-storey, four-bay RC MRFs are selected as case studies. These structures, which share the same geometry, are representative of distinct vulnerability classes in the Mediterranean region and are characterized by different material properties, cross-section dimensions, and detailing. The first case study is a ductile MRF designed according to Eurocode 8 (i.e., a special-code frame), while the second is a non-ductile MRF designed to sustain only gravity loads (i.e., a pre-code frame). The influence of masonry infills on their seismic performance is also investigated. Advanced numerical models are developed to perform cloud-based sequential nonlinear time history analyses using ground-motion sequences assembled by randomly pairing two real records via Latin hypercube sampling. Different structure-specific damage states are considered to derive fragility curves for the undamaged structures, when subjected to a single ground-motion record, and state-dependent fragility curves by considering the additional damage induced by a second ground-motion record within the sequence. Damage-to-loss models are then used to derive mean vulnerability relationships. Results of the analysis show the importance of considering the effect of damage accumulation in the pre-code frames. Moreover, the presence of infills shows an overall positive contribution to the seismic performance of both frame types. Vector-valued vulnerability relationships accounting for the damaging effect of two ground-motion records are finally presented in the form of mean vulnerability surfaces.