The design and investigation of heterometallic d/f-based coordination compounds remain a challenging and attractive goal due to their promising applications in the fields such as information processing and storages and molecular spintronics. In continue of our research on the construction of perspective molecular magnetic materials, in particular with single-molecular magnetic behavior (SMM), a new heterometallic hexanuclear CoIII/DyIII cluster, namely [Co3Dy3(OH)4(piv)6(teaH)3 (H2O)3] (NO3)2•(H2O) (1), has been prepared from the reaction of dinuclear cobalt(II) pivalate with Dy(NO3)3·6H2O and trietanolamine (teaH3) ligand and characterized by elemental analysis, IR spectroscopy, and thermogravimetric studies. A singlecrystal X-ray diffraction analysis showed that cluster 1 crystallizes in the monoclinic space group P21/n and consists of the cation [Co3Dy3(OH)4(piv)6(teaH)3(H2O)3]2+, two NO3 anions and a crystallization water molecule. In the cluster the three CoIII and three DyIII ions are bridged by four  3-hydroxy groups, six pivalate residues and additionally linked by three partly deprotonated teaH2 ligands. Thus, the arrangement of CoIII and DyIII atoms in 1 can be approximated by an assembly of two triangles: the smaller equilateral one defined by three Dy sites with the Dy-Dy distance of 3.9 Å and the larger one formed by Co sites [Co-Co, 6.1 - 6.2 Å] (Fig.1). The dihedral angle between Dy3 and Co3 triangle planes is equal to 37.2°. Since the CoIII-ions are diamagnetic the model for the description of the magnetic behavior of the Co3Dy3 cluster only includes the crystal fields acting on the Dy-ions, the intracluster exchange interaction between the Dy-ions as well as the much weaker exchange coupling between the Dy3 units. The latter interaction is examined within the mean field approach. The crystal field potential for each Dy-ion is calculated in the exchange charge model of the crystal field taking into account the covalence effects arising from the overlap of the 4f-orbitals of the Dy-ions with 2p and 2s orbitals of the oxygen ligands. For the whole cluster quite good agreement is obtained between the calculated and observed values of the magnetic susceptibility as a function of temperature and magnetization as a function of the external magnetic field. At the same time the calculations apparently show that only two of the Dy-ions manifest single molecule magnet behavior, for these ions the zz-component of the magnetic susceptibility χ exceeds appreciably the xx and yy –components which weakly differ. Magnetization tunneling arising from this small rhombicity is suppressed on the experiment by a dc magnetic field. Therefore, the ac signal appears. The surrounding of the third Dy-ion is strongly distorted and this ion does not manifest SMM behavior.