Stretched-exponential decay of persistent photoconductivity (PPC) has been observed in ${\mathrm{Al}}_{0.3}$${\mathrm{Ga}}_{0.7}$As in the temperature region T90 K. The decay time constant and exponent have been measured at different temperatures. Experimental results show that the thermal activated capture of electrons at the DX centers becomes negligible at T40 K. However, a transition from a thermally activated to a nearly-temperature-independent tunneling capture at a temperature on the order of 40 K has been observed for the first time for ${\mathrm{Al}}_{0.3}$${\mathrm{Ga}}_{0.7}$As, which is consistent with the multiphonon-emission model for DX centers of large lattice relaxation.