Three cobalt(II) complexes, [Co(X)(2)(4NOpy)(4)] (X = NCO-, NCS-, and Br-; 4NOpy = 4-(N-tert-butylaminoxyl)-pyridine) were prepared, and their molecular structures were characterized by X-ray structure analysis. The molecular geometry of [Co(X)(2)(4NOpy)(4)] (X = NCO- and NCS-) is a compressed octahedron, in which the counter ions occupy the apical positions with short bond distances of 2.064-2.098 angstrom. In the crystalline state, from plots of chi(mol) vs T and chi'(mol) vs T, [Co(NCO)(2)(4NOpy)(4)] and [Co(NCS)(2)((4)NOpy)(4)] are antiferromagnets with T-N = 4.5 and 15 K, respectively. In frozen solution, on the other hand, both complexes and [Co(Br)(2)(4NOpy)(4)] functioned as single-molecule magnets. The X"(mol) vs T plot for [Co(Br)(2)(4NOpy)(4)] gave a effective activation barrier (U-eff) of 20 K for the reorientation of the spin. From the field dependence of magnetization at various temperatures below 5 K for [Co(X)(2)(4NOpy)(4)] (X = NCO-, NCS-, and Br-) the values of the zero-field splitting parameters, D/k(B), were estimated to be -14, -9.7, and -4.5 K with S = 5/2, respectively. Theoretical studies based on the ligand-field theory model for [Co(NCO)(2)(4NOpy)(4)] gave an exchange coupling parameter, J/k(B), of 29 K and a thermodynamic activation barrier, U, of 60 K.