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Properties of surface acoustic waves (SAWs) in reverse-biased AlGaN/GaN heterostructures on (0001) sapphire substrates were studied by examining the characteristics of SAW filters composed of interdigital Schottky and ohmic contacts. The fundamental and higher frequency SAW signals in measured -parameters were attributed to Rayleigh and Sezawa modes, respectively. The onsets of the SAW signals, which were close to the threshold voltage of HEMTs in the vicinities of the respective filters, changed in response to the spatial variation of the threshold voltage. The onset of Sezawa mode was deeper than that of Rayleigh mode, and the difference in onset was larger for longer SAW wavelengths. These results are possibly explained by the change of the input capacitance of interdigital transducers due to the reverse-bias voltages or by the difference in the distribution of SAW energy between the two modes.