This paper investigates the seismic response of multi-storey cross-laminated timber (CLT) buildings and its relationship with salient ground-motion and building characteristics. Attention is given to the effects of earthquake frequency content on the inelastic deformation demands of platform CLT walled structures. The response of a set of 60 CLT buildings of varying number of storeys and panel fragmentation levels representative of a wide range of structural configurations subjected to 1656 real earthquake records is examined. It is shown that, besides salient structural parameters like panel aspect ratio, design behaviour factor, and density of joints, the frequency content of the earthquake action as characterized by its mean period has a paramount importance on the level of nonlinear deformations attained by CLT structures. Moreover, the evolution of drifts as a function of building to ground-motion periods ratio is different for low- and high-rise buildings. Accordingly, nonlinear regression models are developed for estimating the global and interstorey drifts demands on multi-storey CLT buildings. Finally, the significance of the results is highlighted with reference to European seismic design procedures and recent assessment proposals.