This paper is concerned with the study of propagation of Stoneley waves at the interface of two dissimilar transversely isotropic thermoelastic solids without energy dissipation and with two temperatures. The secular equation of Stoneley waves is derived in the form of the determinant by using appropriate boundary conditions i.e. the stresses components, the displacement components, and temperature at the boundary surface between the two media are considered to be continuous at all times and positions . The dispersion curves giving the Stoneley wave velocity and Attenuation coefficients with wave number are computed numerically. Numerical simulated results are depicted graphically to show the effect of two temperature and anisotropy on resulting quantities. Copper material has been chosen for the medium and magnesium for the medium Some special cases are also deduced from the present investigation.

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