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Biosensors based on surface acoustic waves (SAWs) offer unique advantages due to their high sensitivity, real-time response capability, and label-free detection. The typical SAW modes are the Rayleigh mode and the shear-horizontal mode. Both present pros and cons for biosensing applications and generally need different substrates and device geometries to be efficiently generated. This study investigates and characterizes SAW resonator biosensors on lithium niobate in terms of modes generated and biosensing performance. It reveals the simultaneous presence of two typical SAW modes, the first around 1.6 GHz and the second around 1.9 GHz, differently polarized and clearly separated in frequency, which we refer to as slow and fast modes. The two modes are studied by numerical simulations and biosensing experiments with the glial-fibrillary-acidic-protein (GFAP) biomarker. The slow mode is generally more sensitive to changes in surface properties, such as temperature and mass changes, by a factor of about 1.4 with respect to the fast mode.