An accurate estimation of the maximum inelastic displacement of a structure under seismic excitations is essential to quantitative seismic risk assessment. The seismic performance of existing structures can be evaluated by utilizing inelastic single-degree-of-freedom (SDOF) systems and carrying out nonlinear dynamic analysis. This article develops a probabilistic model of the peak ductility demand of inelastic SDOF systems with various hysteretic characteristics using comprehensive sets of strong ground-motion records observed in Japan. The use of a large database facilitates the systematic investigation of the effects of earthquake type, record selection criteria, seismological parameters, and seismic region on the inelastic seismic demand. Nonlinear dynamic analysis of inelastic SDOF systems is carried out for statistical analysis and probabilistic modeling of the peak inelastic seismic demand. Analysis results indicate that the inelastic seismic demand depends on earthquake type, selection criteria, and seismological parameters to some degree. The most notable differences in inelastic seismic demands are observed for interface records at short vibration periods in comparison with crustal and inslab records; the differences can be explained by different response spectral shapes of the datasets. The inelastic seismic demand for the California crustal records is greater than that for the Japanese crustal records at short vibration periods, whereas the demands are comparable at long vibration periods. The peak ductility demand can be modeled as a Frechet variate, and empirical equations for calculating its statistics are developed, which achieve simplicity and sufficiency in probabilistic seismic risk analysis.