The stationary response of smooth and bilinear hysteretic systems to n
arrow-band random excitations is investigated by using the quasistatic
method and digital simulation. It is shown that the response is quali
tatively different in different ranges of values of the ratio of the e
xcitation central frequency to the natural frequency of the system. In
the resonant zone, the response is essentially non-Gaussian. For bili
near hysteretic systems with strong yielding, stochastic jumps mall oc
cur for a range of values of the ratio between nonresonant and resonan
t zones.