The magnetic anisotropy of the two cyclic hexanuclear Fe(III) clusters [Li subset of Fe6L6]Cl . 6CHCl(3) and [Na subset of Fe6L6]Cl . 6CHCl(3), L = N(CH2CH2O)(3), was investigated. Based on a spin Hamiltonian formalism, the magnetic anisotropy was calculated exactly to first order, i.e., in the strong exchange limit, using Bloch's perturbational approach and irreducible tensor operator techniques. Experimentally, the magnetic anisotropy was investigated by magnetic susceptibility and high-field torque magnetometry of single crystals as well as inelastic neutron scattering. It is demonstrated that torque magnetometry provides a valuable tool for the study of magnetic anisotropy in spin cluster complexes. The experimental data could be accurately reproduced by;he calculations, and the different methods yield consistent values for the coupling constants and zero-field-splitting parameters. Both the anisotropy and the exchange interaction parameter are found to increase with increasing Fe-O-Fe angle.