We have measured the conductivity σxx of GaAs GaAlAs Corbino devices under nonequilibrium conditions in the quantum Hall regime at low frequencies from dc up to 10 kHz. At very low frequencies up to 10-20 Hz, σxx shows a steep decrease from its dc value towards a reduced saturation value. Measurements of the temperature dependence of σxx from 70 mK to 4.2 K revealed a dominance of a conductivity with a temperature dependence σxx ∼exp {- (T0 T)1 2 } typical for variable-range hopping (VRH) at temperatures below 1 K and an additional contribution of thermal activation above 2 K. The characteristic temperature T0 as determined from the VRH-like temperature plot of the conductivity showed also an increase with the frequency and a pronounced decrease with increasing voltage below the breakdown of the quantum Hall effect (QHE). We attribute these results to an effective suppression of the delocalization of electrons in alternating external fields due to a reduced heating and scattering between localization centers. The time scale for this process can be as long as 100 ms. Our data show that the background conductivity σxx at subcritical voltages affects the critical voltage for the breakdown of the QHE. © 2005 The American Physical Society.