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In this work we have fabricated and characterized GaN-based surface acoustic wave filters grown by metal organic chemical vapour deposition (MOCVD) on sapphire substrates. The acoustic wave propagation velocity and piezoelectric electromechanical coupling constant have been determined for different wavelengths. The acoustic velocity and high order propagation mode have been analyzed for different penetration levels of the acoustic wave in the sapphire substrate. The RF filters exhibit an acoustic velocity around 5000 m/s, which is independent from the GaN layer resistivity. In contrast, a strong improvement of the noise level and propagation loss is found in devices fabricated on high resistive GaN. A noise level as low as - 80 dB was measured on prototype devices, which is of the order of the instrument's intrinsic noise. The fundamental Rayleigh mode is accompanied by a high order mode, which is known as the Sezawa mode. The propagation velocity of the Sezawa acoustic wave, ascribed to the presence of sapphire substrate, was almost twice that of the Rayleigh wave, which makes it very interesting for very high frequency applications.