The main features of the local atomic structure of novel Co-x/C-60 (x <= 2.8) complex mixtures were studied using the ab initio B3LYP/6-31G* method for a set of low- and high-energy Co-n(C-60)(m) (n = 1, 2, m = 2, 3) clusters in low and intermediate spin states. For the n = 1 isomers the spin state S = (1)/(2) is energetically preferable, whereas the low-energy isomers of n = 2 have an intermediate spin state of S = 1. The eta(2) (6-6 edge of C-60) type of cobalt ion coordination is preferable for both the n = 1 and n = 2 cases. The eta(2') (coordination with a 6-5 edge) and even the eta(5) (C-5 fragment) types can serve as low- and high-energy intermediates for the cobalt ion's migration around the C-60 cage. Formation of cobalt dimers can be the final stage of evolution of Co-x/C-60 atomic structure approaching the equilibrium atomic geometry.