Complex charge variation processes in low-density, direct-type GaAlAs quantum dots embedded in a type-II GaAs/AlAs bilayer are studied by single-photon correlation measurements. Two groups of excitonic transitions are distinguished in the single quantum dot (QD) photoluminescence spectra, namely due to recombination of neutral and charged multiexcitonic complexes. The radiative cascades are found within each group. Three characteristic time scales are identified in the QD emission dynamics. The fastest one (of the order of 1 ns) is related to excitonic radiative recombination. The two remaining ones are related to the QD charge state variation. The one of 100-ns range (typical blinking time scale) corresponds to random capture of single carriers under a quasiresonant excitation. The slowest processes, in the range of seconds, are related to charge fluctuations in the surrounding of the dot.