The propagation of leaky Rayleigh waves under the influence of viscous damping and heat conduction in boundary layers is studied using the matched asymptotic method. Viscosity of the fluid is considered unimportant except in a thin viscous boundary layer at the interface. A new characteristic equation is obtained in which the effect of boundary layer is shown by terms associated with R−1/2=(ων)1/2/ct, where R is the Reynolds number, ω is the frequency, ν is the kinematic viscosity of the fluid, and ct is the shear velocity of the solid substrate. One of the numerically obtained solutions gives the leaky Rayleigh wave speed and the attenuation coefficient. It is shown that, together with radiation, viscosity and heat conduction in the boundary layer also affect the attenuation of the leaky Rayleigh waves. Furthermore, it is shown that, because of the effect of the viscous boundary layer, the attenuated leaky Rayleigh wave speed can be smaller than the Rayleigh wave speed at the interface of a vacuum and a solid substrate. A critical Reynolds number of about 2500 is found beyond which a viscous boundary layer stops influencing leaky Rayleigh wave propagation. Finally, a new wave mode sustained by the viscous boundary layer alone is found in the limit of a small fluid–solid density ratio. This mode exists for appropriate frequency and layer thickness combinations. For air, the corresponding propagation speed is shown to be higher than the sound speed and the corresponding attenuation is significant. These results may be used to improve our interpretation of acoustic signature of materials.