In addition to the persistent photoconductivity (PPC) attributed to DX centers in GaAs delta-doped with Si, a weak PPC (WPPC) with a PPC carrier density independent of Si-doping concentration has been generally reported at ambient atmosphere, but the nature of the deep states responsible has not been elucidated. Here, we present the results of a detailed study of the WPPC in δ-GaAs:Si at low-doping densities, NSi≈1–3×1012 cm−2, and ambient pressure. It is concluded that the WPPC does not arise from DX centers but from another deep defect, which is DX-like in the sense that it can be metastably excited. The presence of two distinct DX-like states is apparent from two separate annealing temperatures of the PPC, Ta≈50 K and Tb≈230 K; to the best of our knowledge, the latter is the highest annealing temperature observed in the AlGaAs:Si system.