The use of outriggers in tall buildings is a common practice to reduce response under dynamic loading. Viscous dampers have been implemented between the outrigger and the perimeter columns, to reduce vibrations produced by strong winds. However, its behaviour under strong earthquakes has been not yet properly investigated. Strong earthquakes introduces larger amount of energy into the building’s structure, compared to moderate earthquakes or strong winds. In tall buildings, such seismic energy is dissipated by several mechanisms including bending deformation of the core, friction between structural and non-structural components, and eventually, damage. This research focuses on the capability of tall buildings equipped with damped outriggers to undergo large deformations without damage. In other words, when ground motion increases due to strong earthquakes, the dampers can be assumed to be the main source of energy dissipation whilst the host structure displays an elastic behaviour. These investigations are based on the assessment of both the energy demands due to large-earthquake induced motion and the energy capacity of the system, i.e. the energy capacity of the main components, namely core, outriggers, perimeter columns and dampers. The objective of this research is to determine if the energy dissipated by hysteresis can be fully replaced by energy dissipated through the action of passive dampers. The results show that the use of a set of outriggers equipped with oil viscous dampers increases the damping ratio of tall buildings in about 6-10%, depending on the loading conditions. As the ground motion becomes stronger, viscous dampers effectively reduce the potential of damage in the structure if compared to conventional outriggers. However, the use of dampers cannot entirely prevent damage under critical excitations. Combining a damped outrigger at 0.5 of the total building’s height (h), with a conventional outrigger at 0.7 h is more effective in reducing hysteretic energy ratios and economically viable if compared to a single damped outrigger solution.