This paper investigates the behavior of a typical Chilean reinforced concrete wall building under sequential earthquake and tsunami actions using a double pushover analysis approach. A real concrete wall structure that was damaged after the Mw = 8.8 2010 Maule earthquake is considered as a case study building and a simplified nonlinear finite element model of a fictitious slice of the building is subjected to earthquake and tsunami loading in sequence. The analysis of the building under these loadings consists of three stages: the structure is first subjected to seismic loading by means of a pushover analysis until a specific damage state is reached; then a pushover with the same load pattern but in the opposite direction is applied until the shear at the base is zero; and finally, the building is subjected to tsunami loading by means of a variable depth pushover analysis until the maximum capacity is reached. Different tsunami load cases are considered in this study, varying the Froude number and the direction of the tsunami loading. The results show that the tsunami response of the building is mainly dependent on the Froude number of the tsunami flow; however, when the seismic damage is severe, the tsunami capacity of the building is found to be reduced. This is more likely to occur when the effect of the tsunami increases the damage previously induced by the earthquake in the same direction.