We have re-examined the results and analysis of capacitance transient spectroscopy measurements made on modulation-doped heterostructures suitable for the fabrication of field-effect transistors. It is seen that conventional analysis of data can lead to erroneous results and a new model, which includes the contribution of the capacitance at the heterointerface, is presented. Most of the observed anomalous behavior related to trap emission can now be explained. Six main electron traps are present in single-layer Al x Ga 1-x As, grown by molecular-beam epitaxy, and in device-quality GaAs-Al x Ga 1-x modulation-doped heterostructures. These range in energy from 0.40 to 0.91 eV in thermal ionization energy. The well known D-X center in Si-doped Al x Ga l-x As layers is composed of two closely spaced levels, DX1 and DX2, with ionization energies of 0.48 and 0.52 eV, respectively. At very low Si,doping levels, only DX2 is dominant, but at doping levels > 10 18 cm -3 , both DX1 and DX2 become comparable in concentration. The optical ionization properties of these levels were also measured and it is seen that the optical lineshapes differ markedly for the two centers. The peak photoionization cross sections occur at spectral energies of 1.25 and 1.38 eV for DX1 and DX2, respectively. The nature and symmetry of the centers have been studied by measurements on layers of different orientations.