The propagation rules of double orthogonal polarization and coinciding centre Gaussian beams which propagate in nonlocal nonlinear planar waveguides are studied with analytical method. The evolution equations of two beam various parameters and two critical powers are obtained, the values of which relate to the coupling coefficient and the degree of nonlocality. In the case of the unique refraction, the critical powers of two beams are the same when the initial beam widths are equal to each other. When the initial power equals the critical power, two orthogonal polarization Gaussian linear spatial solitons are derived, which are irrelevant with the degree of nonlocality of the medium. For the strongly nonlocal case, under the condition of unique refraction, the analytical evolution expressions of various parameters of beams are obtained. When the total power is equal to the critical power, and the two beam powers are not the same, two orthogonal polarization Gaussian types of breathers are obtained, the higher power beam width compressing oscillates periodically and the lower power beam width broadening oscillates periodically.