Quantized chaotic systems are generically characterized by two energy scales: the mean level spacing and the bandwidth. This implies that with respect to driving such systems have an adiabatic, a perturbative and a non-perturbative regimes. A \"strong\" quantal non-perturbative response effect is found for systems that are described by random matrix theory models. Is there a similar effect for quantized \"chaotic\" systems ? Theoretical arguments cannot exclude the existence of a \"weak\" non-perturbative response effect, but detailed numerical investigations results in an unexpected degree of semiclassical correspondence.