We have studied hole transport in amorphous As2Te3(a‐As2Te3) films by time‐of‐flight (TOF) and transient field‐effect (TFE) measurements. Since the mobility gap of this material is small, the TOF experiments could be carried out only at temperatures below 200 K. Transport appears to be dispersive, due to multiple trapping in the valence‐band tail. In order to extend the observations to higher temperature and longer times, we have developed a new technique, the TFE. A careful analysis shows that TFE data can be dispersive even if transport is nondispersive, because a long thin‐film transistor is equivalent to a transmission line. Nevertheless, the resulting data can be used to characterize the density of states beyond the mobility edge. We find that multiple trapping indeed predominates, and the valence‐band tail is exponential with a characteristic temperature of about 290 K. This is somewhat lower than indicated by TOF data, probably because hopping transport predominates at low temperatures. The long‐time transients can be associated with either neutral defect interconversion and a continuous distribution of decay times or deep traps near the semiconductor‐oxide interface. However, the ultimate disappearance of the response reflects the effects of Fermi‐level pinning by valence alternation pairs with a negative effective correlation energy, as expected.