This paper presents a comprehensive comparison of different dynamic and static approaches for assessing building performance under sequential earthquakes and tsunami. A 10-storey reinforced concrete seismically designed Japanese vertical evacuation structure is adopted as a case study for the investigation. The case study building is first assessed under sequential earthquake and tsunami nonlinear response history analyses: the first time this is done in the literature. The resulting engineering demand parameters are then compared with those obtained when the analysis procedure is systematically simplified by substituting different static approaches for the nonlinear response history analyses in both the earthquake and tsunami loading phases. Different unloading approaches are also tested for the cases when an earthquake pushover is adopted. The results show that an earthquake nonlinear response history analysis, followed by a transient free vibration and a tsunami variable depth pushover, provides the best alternative to full dynamic analyses in terms of accuracy and computational efficiency. This structural analysis combination is recommended and has the advantage that it does not require the tsunami inundation time history to be known in advance. The proposed double pushover approach is instead deemed only suitable for the collapse assessment of regular low to mid-rise buildings and for the development of collapse fragility functions. An important observation made is that sustained earthquake damage seems not to affect the tsunami resistance of the case study building when the fully dynamic analysis is carried out for the sequential loading. This observation will be the subject of future work.