The rotational Smoluchowski equation for the orientational distribution function of two identical linear molecules or dipoles with anisotropic interaction is solved by expansion in terms of a limited set of eigenfunctions of the operator for free rotational diffusion. The equilibrium self-correlation and pair time-correlation functions of the two axial unit vectors or dipole moments are evaluated for the special case of electrostatic or magnetostatic dipole interaction. The interactions appreciably influence the relaxation behavior.