Scanning capacitance spectroscopy has been used to characterize, at the nanoscale, the frequency-dependent response of surface charge and of charge in the two-dimensional electron gas of an AlxGa1−xN/GaN heterostructure field-effect transistor structure. dC/dV spectra were measured in a scanning capacitance microscope with a voltage signal consisting of a triangle wave at frequencies of 1 – 50 Hz applied to the sample. The spectra were obtained in the dark (except for 600 nm laser light from the scanning capacitance apparatus) and under illumination. Measurements were performed in the vicinity of and away from charged threading dislocations visible in scanning capacitance images. In the absence of illumination, the dC/dV data indicate that electrons are trapped at or near the AlxGa1−xN surface, consistent with suggestions in the literature that a high density of surface states exists on the free AlxGa1−xN surface. Frequency-dependent measurements show that emission times for these traps can be as long as several hundred ms. In the presence of illumination, reduced electron trapping is observed. The nature and behavior of trap states in the vicinity of threading dislocations is found to differ significantly from that in regions between dislocations for measurements in the dark, and suggest that the electrostatic potential due to the charged threading dislocation is negligible at the surface.