The kinetics of persistent photoconductivity (PPC) in Al0.3Ga0.7As and Zn0.3Cd0.7Se has been investigated. The PPC relaxation behaviors in both materials can be well described by stretched-exponential functions, IPPC(t)=IPPC(0)exp[-(t/)] (<1). For Al0.3Ga0.7As, the relaxation-time constant , as a function of the relative photoexcited electron concentration n, is measured through the variation of the excitation photon dose in the temperature region T10 K. At low temperatures, we found that in Al0.3Ga0.7As, decreases and reaches a minimum value as n increases in the low-concentration region but it increases with increasing n in the higher-concentration region. Such a turning-over behavior observed in Al0.3Ga0.7As is believed to be due to the crossover from a nondegenerate to a degenerate regime as the electron concentration increases. At higher temperatures, observed in Al0.3Ga0.7As decreases monotonically with increasing electron concentration, which is consistent with the fact that the degenerate carrier concentration is more difficult to attain at higher temperatures. The PPC-buildup transients in Al0.3Ga0.7As and Zn0.3Cd0.7Se have also been measured and formulated at different conditions and are shown to be very different. These results have shown that the PPC-buildup transients contain information not only about electron excitation but also electron recapture. The photoionization cross section of DX centers, DX, in Al0.3Ga0.7As has been obtained from the PPC-buildup-transient measurements. The experimental results indicate that the transport properties in Al0.3Ga0.7As are controlled by DX centers as expected, but in II-VI semiconductor alloys in the low-electron-concentration region they are governed nonetheless by tail states induced by compositional fluctuations.