In n-GaAs/InGaAsP and p-Ge/GeSi quantum well heterostructures excited by both the picosecond broad band and the nanosecond narrow band pulses of THz radiation the relaxation times of the impurity photoconductivity were measured. In one of the sample Ge/GeSi this more narrow quantum well we observed the first time increases maximum relaxation time from 9 to 14 ns at the narrow band THZ radiation frequency decrease from 60 cm−1 down to 25 cm−1 that can be explained by a dispersion of shallow acceptor binding energies. The frequency of 60 cm−1 nearly corresponds to the binding energy of acceptors situated nearby Ge QW center while that of 25 cm−1 corresponds to ionization energy for the hole (in Ge QW) bound with a remote acceptor ion in the center of GeSi barrier. We explain the observed larger relaxation time for the acceptor with lower binding energy by an enhanced probability for the hole captured by an excited impurity state to be thermally activated again into the valence band.