The coexistence of the DX center with nonmetastable bound states of the ordinary substitutional configuration of the donor impurity is extensively investigated in Si-doped ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As samples having different x AlAs molar fractions in the direct gap region. The occupation of nonmetastable states is evidenced by comparing the ${\mathit{n}}_{\mathit{CV}}$ ``electron density,'' as derived from capacitance-voltage measurements in Schottky diodes, with the ${\mathit{n}}_{\mathit{H}}$ Hall density. In samples of compositions not far from the direct-to-indirect gap transition and with doping levels in the ${10}^{18}$-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ range, a nonmetastable state SX, degenerate in energy with the conduction band, can reach a significant occupancy when the saturated persistent photoconductivity condition is approached during low-temperature photoionization of DX centers. On the other hand, when the free-electron density is smaller than a critical density of a few ${10}^{16}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, electrons freeze out into a localized S\ensuremath{\Gamma} state, or into a low mobility impurity band, linked to the \ensuremath{\Gamma} conduction-band edge. A finite occupancy of the SX or S\ensuremath{\Gamma} state gives rise to a significant ${\mathit{N}}_{{\mathit{D}}^{0}}$ density of substitutional donors in the neutral ${\mathit{D}}^{0}$ charge state having a strongly correlated spatial distribution. Electron capture into donor states, DX or not, has a spatially selective character, as can be evidenced by low-temperature mobility data under conditions where impurity scattering dominates. For DX centers, this is demonstrated by the hysteretic behavior of low temperature (${\mathit{T}}_{0}$) ${\mathrm{\ensuremath{\mu}}}_{\mathit{H}}$ vs ${\mathit{n}}_{\mathit{H}}$ data, where any given ${\mathit{n}}_{\mathit{H}}$ value is reached through DX center photoionization steps or through electron capture via a proper thermal cycling. When ${\mathit{N}}_{{\mathit{D}}^{0}}$ is negligible the hysteresis amplitude is maximum. However, whenever ${\mathit{N}}_{{\mathit{D}}^{0}}$ reaches significant values, either at the ${\mathit{T}}_{0}$ temperature or during the thermal cycle, the hysteresis amplitude vanishes. This is systematically observed in all the cases where the occupation of SX or S\ensuremath{\Gamma} states is independently demonstrated through the analysis of ${\mathit{n}}_{\mathit{CV}}$ and ${\mathit{n}}_{\mathit{H}}$ data. Two diverse complementary effects are proposed to explain the observed vanishing of the hysteresis amplitude. \textcopyright{} 1996 The American Physical Society.