The bimetallic series MM'(EDTA).6H2O ([MM'] = [MnCo[, [MnNi], [MnCu], [CoCo], [CoNi], [CoCu], [NiNi]) comprises zigzag chains built up with alternated "hydrated" and "chelated" sites bridged by carboxylate groups: ...-M(H2O)4O2---M'-(EDTA)-M(H2O)4O2---M'(EDTA)-... The g tensors of cobalt(II) on both sublattices are determined from a single-crystal EPR study on Co-doped [ZnZn] samples. On the other hand, a single-crystal EPR study of the bimetallic chain [CoCu] is reported. The angular dependence of the resonance fields are simulated from a triplet spin state with a large zero-field splitting of modulus \D\ almost-equal-to 0.3 cm-1, which is almost parallel to the g tensor of cobalt. This result provides some evidence of the presence of cobalt-copper exchange-coupled pairs within the chain, constituting the first spectroscopic proof of dimerization in this chain; furthermore, it emphasizes the anisotropic nature of the exchange, which is in good agreement with the spin anisotropy of cobalt. The factors determining the dimerization of this and other cobalt-containing chains of the EDTA series are discussed.