The characteristics of surface acoustic waves (SAWs) in GaN layers grown on c-plane sapphire are investigated. Besides Rayleigh mode, Sezawa and Love modes, which are confined in the nitride layers, arise because of the slow sound propagation in GaN compared with the substrate. In addition, pseudo-SAWs leaking into the bulk are observed. The trigonal crystal symmetry of sapphire not only leads to an anisotropic propagation of the SAWs in the heterostructures, despite the isotropic elastic properties in the c-plane GaN, but also mixes their polarization even for the propagation along high-crystal-symmetry directions. Love modes, which are normally piezoelectrically inactive, can be excited by interdigital transducers through this polarization mixture. The nonzero value of the elastic coefficient c(14) of sapphire is indicated to be the origin of the coupling of sagittal and shear horizontal displacements.