The effectiveness of the isolation system installed on the supports of the secondary structures mounted on a multistorey structure is evaluated for reducing the seismic response to various earthquakes in this study. The responses of the support-isolated secondary structure in a fixed-base multistorey structure are compared with those of a fixed support secondary structure in-fixed-base and base-isolated multistorey structures to investigate the reduction of the seismic response. Three analytical models are used to evaluate the effectiveness of the isolation system: a fixed-base multistorey structure with fixed-support secondary structure, a base-isolated multistorey structure with a fixed-support secondary structure, and a fixed-base multistorey structure with a support-isolated secondary structure. The seismic responses are analysed to identify their behaviour due to the characteristics of input ground motion with various peak acceleration and frequency content. The efficient stiffness of the base-isolator for reducing the seismic response is also evaluated for several earthquakes through the acceleration - displacement relationship.