We have measured the generation-recombination noise from the donor-related DX centers in current biased GaAs/AlxGa1-xAs heterostructures from 1 Hz to 25 kHz and from 77 to 330 K. A significant noise contribution from these traps is observed even at Al mole fractions below 0.2, where the trap level is resonant with the conduction band. The activated behavior of the noise spectrum from this resonant level is very similar to that observed at higher Al mole fractions, when the level lies deep in the fundamental gap. This result can be predicted, based on the recently elucidated relationship of the trap level to the band structure of AlxGa 1-xAs. In accordance with other experimental results, the noise spectra demonstrate that the emission and capture kinetics of the level are unperturbed by its resonance with the conduction band. We briefly discuss some implications of these results for heterostructure transistor design.