In order to enable appropriate assessment of the seismic response of ancillary elements within multi-storey frames, it is necessary to provide reliable practical approaches for predicting the imposed displacement and acceleration demands. In this paper, the elastic and inelastic seismic response of non-structural ancillary components within multi-storey steel frames is examined. For this purpose, a large set of steel moment framed structures, with and without irregularities, is considered. The frame structures, which are designed according to Eurocode 8, are described in detail in terms of their configurations, member sizes, and dynamic characteristics. Within these frames, non-structural components, characterised by various periods and strength reduction factors are mounted at individual floors and assessed in terms of both their displacement and acceleration response under seismic loading. Detailed nonlinear dynamic time-history analyses are carried out under a large suite of ground motion records. It is shown that various modifications to current design provisions are necessary to capture the response in a reliable manner. Based on the findings, a new model is proposed for predicting the seismic displacement and acceleration response of non-structural ancillary components mounted within the floors of both regular and irregular multi-storey steel frames, with due account for the inelastic behaviour of both the ancillary elements and the frames.