New tetranuclear and octanuclear mixed-valent cobalt(II/III) pivalate clusters, namely, [NaCo4(O2CCMe3)(6)(HO2CCMe3)(2)(teaH)(2)(N-3)]center dot 2H(2)O (in two polymorphic modifications, 1 and 1a) and [Co-8(O2CCMe3)(10)(teaH)(4)(N-3)](Me3CCO2)center dot MeCN center dot H2O (2) have been synthesized by ultrasonic treatment of a dinuclear cobalt(II) pivalate precursor with sodium azide and triethanolamine (teaH3) ligand in acetonitrile. The use of Dy(NO3)(3)center dot 6H(2)O in a similar reaction led to the precipitation of a tetranuclear [NaCo4(O2CCMe3)(4)(teaH)(2)(N3)(NO3)(2)(H2O)(2)]center dot H2O (3) cluster and a heterometallic hexanuclear [Co3Dy3(OH)(4)(O2CCMe3)(6)(teaH)(3)(-)(H2O)(3)](NO3)(2)center dot H2O (4) cluster. Single -crystal X-ray analysis showed that 1 (1a) and 3 consist of a tetranuclear pivalate/teaH(3) mixed-ligand cluster [(Co2Co2III)-Co-II( O2CCMe3)(4)(teaH)(2)(N-3)](+) decorated with sodium pivalates [Na(O2CCMe3)(2)(HO2CCMe3)(2)](-) (1 or la) or sodium nitrates [Na(NO3)(2)](-) (3) to form a square -pyramidal assembly. In 2, the cationic [Co-8(O2CCMe3)(10)(teaH)(4)(N-3)](+) cluster comprises a mixed-valent {(Co4Co4III)-Co-II} core encapsulated by an azide, 4 teaH(2-) alcoholamine ligands, and 10 bridging pivalates. Remarkably, in this core, the mu(4)-N-3(-) ligand joins all four Co" atoms. The heterometallic hexanuclear compound 4 consists of a cationic [(Co3Dy3III)-Dy-III (OH)(4)(O(2)CCMe(3)e(3))(6)(teaH)(3)(H2O)(3)](2+) cluster, two NO3- anions, and a crystallization water molecule. The arrangement of metal atoms in 4 can be approximated as the assembly of a smaller equilateral triangle defined by three Dy sites with a Dy center dot center dot center dot Dy distance of 3.9 angstrom and a larger triangle formed by Co sites [Co center dot center dot center dot Co, 6.1-6.2 angstrom]. The interpretation of the magnetic properties of clusters 2-4 was performed in the framework of theoretical models, taking into account the structural peculiarities of clusters and their energy spectra. The behavior of clusters 2 and 3 containing Co-II ions with orbitally nondegenerate ground states is determined by the zero -field splitting of these states and Heisenberg exchange interaction between the ions. To get a good understanding of the observed magnetic behavior of cluster 4, we take into consideration the crystal fields acting on the Dy-III ions, the ferromagnetic coupling of neighboring Dym ions, and the intercluster antiferromagnetic exchange. For all examined clusters, the developed models describe well the observed temperature dependence of the magnetic susceptibility and the field dependence of magnetization. The computational results apparently show that in cluster 4 two Dy-III ions with similar nearest surroundings demonstrate single -molecule -magnet (SMM) behavior, while the strong rhombicity of the ligand surrounding hinders the SMM behavior of the third Dym ion.