In some Rare Earth-Transition Metals compounds the anisotropy shows a complex behaviour: easy direction of magnetization out of the crystallographic axis, large high order anisotropy constants and jumps in the magnetization curves were measured. We observed that these effects were present in systems where the anisotropies of the various sublattices were strong and opposite (axial vs. planar) and where the exchange was not strong enough to completely dominate. We developed a quantitative model taking into account the competition between the exchange and the difference in the anisotropies allowing for possible canting between the sublattice magnetizations. We found that a canting angle is indeed possible although it is small and dependent on the orientation of the resultant magnetization. However the possibility of deviating from the collinear order results in an energy relaxation that greatly distorts the shape of the anisotropy energy surface. Consequently the anisotropy of the resulting system cannot be described by the sum of the anisotropy constants of the individual sublattices: strong corrections and higher order terms must be taken into consideration. These corrections, calculated from realistic values of the parameters, turn out to have the right sign and magnitude so as to justify the observed phenomena.