This work discusses the efficiency of Eurocode-compliant, steel moment resisting frame buildings (MRF) sited in combined wind and seismic environments. MRF systems are used widely in European engineering practice to withstand lateral loads. Following current code practice that adheres to capacity design principles, MRF dissipate seismic energy through yielding of their beams. However, the strength or stiffness of seismically ductile members of flexible buildings tends to be governed by wind demands. Herein, we highlight the limitations of the current, single hazard design methodology, and assess the structural efficiency of Eurocode-compliant tall MRF buildings subjected to earthquake and wind excitation. Key findings are derived from the assessment of a 20-story steel MRF building, sited in combined seismic and wind environment in Northern Italy, and detailed as per the Eurocode. We apply a comprehensive assessment framework, to quantify the system performance under recurring winds and earthquakes. Performance objectives and acceptance criteria for the multi-hazard response are mapped to admissible damage states. We use detailed, lumped plasticity models of the MRF archetype in OpenSees, along strong ground motion and local aerodynamic data to predict efficiently the multi-hazard response at the design level and beyond.