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This paper presents some propagation properties of QLLSAW propagating on Y-rotated cut quartz substrates, such as the substrates at Euler angles [0°, 124°, 50°], [0°, 126°, 50°], [0°, 132°, 50°] etc. The advantages of properties of quasi-longitudinal leaky surface acoustic waves (QLLSAW) along these directions are small propagation attenuation (less than 10 -4 dB/λ), small power flow deviation and high phase velocity (can be up from 6,200 m/s to 7,000 m/s). Frequency responses of experimental devices are smooth enough to be applied in practice and the leaky surface shear wave signal cannot be observed in the frequency response. The temperature coefficients on these substrates are also investigated.