AbstractAsymmetrically yielding single‐degree‐of‐freedom elastoplastic systems are subjected to simulated accelerograms based on El Centro‐NS, 1940 ground motion (wide frequency band) to calculate the corresponding ductility demands. Results are compared with those corresponding to simulated accelerograms of the SCT‐EW, 1985 Mexico earthquake (narrow frequency band) obtained in a previous work. Results obtained reveal that the characteristics of the excitation influence the response of asymmetrically yielding structures and that the differences found on responses corresponding to both earthquakes are due to frequency content, duration and/or intensity of motion. The effect of the latter concepts is studied using modulating sinusoidal excitations as well as accelerograms recorded on soft and hard soils of Mexico City.Two alternate expressions are proposed to evaluate the increase in ductility demands of structures with asymmetric force‐displacement curves with respect to symmetric ones. Those expressions take into account motion intensity and duration, as well as seismic design