The coupling effects of secondary inelastic systems on the primary and secondary seismic responses is the focus of this work. The interaction between a single-degree-of-freedom secondary system and a single-degree-of-freedom primary system is analyzed. The main objective is to determine the dynamic response of untuned and tuned systems when one or both systems behave inelastically. The Wilson-θ numerical integration method is used to determine the maximum response of the systems under coupled and uncoupled analyses. A total of 15 actual strong ground motion time histories are used in order to perform a statistical analysis. The influence of the A/V ratio (ratio of the peak ground acceleration to the peak ground velocity) of the earthquake records on the response using 3% and 5% damping ratio, is investigated. The influence of various parameters on the system response are considered. The primary fundamental frequencies of 10.0, 5.0, 1.0, and 0.2 Hz are used with frequency ratios (ratio of the secondary fundamental frequency to the primary secondary fundamental frequency) of 0.1 to 5.0 to study the effect of untuned systems. Special attention is given to the closely-tuned systems. The degree of inelasticity is varied by using yield level factors of 1.0, 0.75, 0.50 and 0.25. The emphases is placed on the behaviour o-F el aster-plastic systems. Mass ratios o-F 0.1, 1.0, 2.0, 5.0 and 10.0% are used. The results indicate that untuned systems can experience responses which are as important as tuned systems. The -Frequency content o-F the earthquake records is not an important -Factor. The eFFect o-F the mass ratio and yield level is mostly limited to systems with -Frequency ratios oF 0.8 to 1.25. / Thesis / Master of Engineering (ME)