[en] The effects of the two lowest-order uniaxial anisotropy fields on the phase diagrams of the classical m-vector spin glass are analyzed. The model is defined in terms of infinite-range interactions and the replica approach is used to study the system. The replica-symmetric phase diagrams present qualitative modifications with respect to those with no uniaxial anisotropies; new features, in particular, reentrance effects arise. In some cases, the reentrant critical frontiers are totally inside the region of instability of the replica-symmetric solution and may disappear within more general parametrizations, whereas in other cases, they coincide with the limit of stability of such a solution and should persist under replica-symmetry breaking