The direction of spontaneous magnetization in rare-earth compounds and alloys is the result of a delicate balance between the magnetic and the electrostatic crystal field interactions on one hand and the relative strengths of the various terms in the crystal field Hamiltonian. At a site of cubic symmetry there are only two terms in the crystal field (fourth order and sixth order); Lea Leask and Wolf (1962) have introduced the parameter x to quantify the relative strength of these two terms. In the present work a parameter R is introduced to quantify the relative strengths of the magnetic and the electrostatic interactions. Diagrams of the computed direction of spontaneous magnetization as a function of the parameters R and x for all the allowed values of J between 3 and 8 have been obtained. It is found that, in agreement to what is observed experimentally, the direction of spontaneous magnetization is in general along one of the principal crystallographic orientations. For all values of J investigated each of the three orientations <100>, <110>, and <111> can be the direction of spontaneous magnetization for some values of the parameters x and R. It is found that at the boundaries between the regions in the {R,x} parameter space there are three possible types of behaviors for the direction of spontaneous magnetization. The direction of spontaneous magnetization can either rotate continuously from one crystallographic orientation to the other or display a sudden jump from one orientation to the other at a critical value of {R, x}. Two One situations have been observed in the latter case. At the critical value the plane containing the two crystallographic orientations involved becomes a degenerate plane or, at the critical value the two orientations are degenerate and there is a region close to the boundary where there is an unstable equilibrium orientation for the direction of spontaneous magnetization.