The dynamic response of single degree of freedom nonlinear systems subjected to earthquake motions is considered with the purpose of deriving factors for constructing inelastic design spectra, and to evaluate the effect of damping combined with inelastic behavior and the influence of the type of material nonlinearity on inelastic response. Inelastic response spectra for elastoplastic systems with 2, 5, and 10 percent damping, and for bilinear and stiffness degrading systems with 5% damping, are computed for a number of frequencies ranging from about 0.03 cps to 35 cps, for ductility values from 1 to 10, and for ten strong-motion earthquake records. A statistical procedure is developed to analyze the data; from this analysis, factors for deriving the characteristic trapezoidal design spectrum are obtained. Such factors reflect, in an explicit manner, the effect of the various parameters considered.