This thesis is concerned with passive control systems for seismic protection of building structures, with special emphasis on elastomeric bearings, viscous dampers and tuned mass dampers. Both mathematical modeling and earthquake response analysis techniques are presented for this class of problems. Earthquake response simulations are carried out for a six-story L-shaped building equipped with these protective systems and subjected to three real earthquake ground excitations, namely the El Centro 1940, Orion Blvd 1971 and Capitola 1989 earthquake records. Both deterministic and stochastic earthquake ground excitations are considered. The performance and effectiveness of these passive protective systems are studied mainly in the time domain with some considerations of the frequency domain. Based on all analyses performed and for the particular building structure considered, it is found that base isolation is very effective in reducing the seismic structural response, especially if it exhibits a nonlinear hysteretic behavior, since in addition to decoupling the frame structure from the ground motion, it dissipates the earthquake input energy through hysteretic action. Tuned-mass damping is less effective than viscous damping in reducing the structural response to earthquake excitations. The results also show that the characteristics of the earthquake ground excitation represent a very important factor which influences the performance of the three passive earthquake protective systems studied herein, especially of the tuned-mass damper system.