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The study of the factors governing the magnetic anisotropy in transition metal compounds is directly related to the problem of the rational design of new single molecular magnets. In this view the systems comprising ions with unquenched orbital angular momenta seem to be quite attractive. Among them the exchange coupled polynuclear compounds of cobaltII are especially interesting as the systems exhibiting strong orbital contributions to the magnetic moments and thus strong magnetic anisotropy. This orbital magnetism arises from the ground orbital triplet 4T1 of each cobaltII ion in a cubic crystal surrounding. The study of the magnetic properties of the magnetic materials containing cobaltII ions always called many difficult theoretical questions which remain still open. These questions arise mainly from the intrinsic complexity that is peculiar to the problem of the magnetic exchange in the presence of the …