We proposed that the disorder induced gap states (DIGS) can be responsible for the threshold voltage (V-th) instability in Al2O3/AlGaN/GaN metal-oxide-semiconductor high-electron-mobility transistors. In order to verify this hypothesis, we performed the theoretical calculations of the capacitance voltage (C-V) curves for the Al2O3/AlGaN/GaN structures using the DIGS model and compared them with measured ones. We found that the experimental C-V curves with a complex hysteresis behavior varied with the maximum forward bias and the sweeping rate can be well reproduced theoretically by assuming a particular distribution in energy and space of the DIGS continuum near the Al2O3/AlGaN interface, i.e., a U-shaped energy density distribution and exponential depth decay from the interface into Al2O3 layer (up to 4 nm), as well as suitable DIGS capture cross sections (the order of magnitude of 10(-15) cm(2)). Finally, we showed that the DIGS model can also explain the negative bias induced threshold voltage instability. We believe that these results should be critical for the successful development of the passivation techniques, which allows to minimize the V-th instability related effects. Published by AIP Publishing.