Asymptotic equations are derived for all four (three diagonal and one off-diagonal) components of the Irving-Kirkwood pressure tensor in a wedge-shaped film of a fluid located between solid phases characterized by dispersion forces. The equations describe the dependence of the aforementioned components on the position inside the film at large distances from the solid surfaces. It is shown that, when the walls of a slit are of different natures, the pressure tensor depends not only on the opening angle of the wedge-shaped slit, bus also on the position of the interface between the solids in contact outside of the slit. As a consequence, the symmetry of the spatial dependence of the tensor components with respect to the median plane is violated.