Accuracy and efficiency are investigated for several different methods to obtain time histories of response of coupled linear or nonlinear systems subjected to seismic excitations. Solutions for the composite system of equations are considered, as well as iterative solutions of coupled equations for primary and secondary subsystems. Two new formulations involving stiffness coupling of the subsystems are introduced. For linear systems, the Newmark method for the composite system seems generally to give slightly better results than the primary-secondary methods. For nonlinear systems, the direct stiffness coupled subsystem approach is found to be more efficient than the other methods, especially if the nonlinearity is in one of the smaller subsystems. It is also shown that only Rayleigh damping can simultaneously lead to classical normal modes for the composite and for each subsystem without imposing any restrictions on the stiffness or mass matrices.