We critically reconsider the analysis (performed within the Kambe’s model in [1]) of the magnetic measurements for the two novel polyoxotungstates, (n-BuNH3)12[(CuCl)6-(AsW9O33)2]·6H2O and (n-BuNH3)12[(MnCl)6(SbW9O33)2]·6H2O [1]. Analysis of the magnetic susceptibility and magnetization for 12+ Cu6 and 12+ Mn6 hexagons based on the exact diagonalization of isotropic exchange Hamiltonian supplemented by anisotropic terms (based on Magpack software [2]), shows that the best fit first-neighbor coupling parameters are J = 35 cm -1 and 0.55 cm -1 for 12+ Cu6 and 12+ Mn6 clusters. We got also perfect fit to the experimental data for the field dependence of magnetization at 1.8 K. We discuss also the symmetry assignments of exchange multiplets to the exact SΓ terms (full spin S and irreducible representation Γ of the point group) and correlate the results with the selection rules for the anisotropic magnetic contributions [3]. The antisymmetric (AS) exchange is shown to appear in orbitally degenerate multiplets as a first order perturbation and gives rise to an easy axis of magnetization along C6 axis. EPR spectra of the lowest lying orbital doublet ( 5E) are simulated with the use of the pseudo-angular momentum representation, which determines the angular dependence, selection rules and the intensities of the transitions. It is shown that the AS exchange introduces strong 39 magnetic anisotropy, i.e. dependence on the orientation of the field with respect to the C6 axis (q) of the hexagon. In parallel field the levels exhibit linear field dependence, increase of the angle q mixes the levels and finally at q=p/2 they become degenerate (figure). Strong field in the plane (hard axes) fully reduces the AS exchange (dashed lines).figure