Lithium-based cells LiCo2O4 have been characterized by magnetic techniques, looking at the influence of the partial substitution of cobalt by 3d or 4d transition metal elements (Fe, Ni, Cu, Cr, Mo). The non-substituted compound LiCo2O4 behaves as an antiferromagnet, with a Neel temperature T-N of 30 K, although antiferromagnetic interactions are much more important, as suggested by a Weiss parameter Theta of the order of -225 K. In the solid solution Li(NixCo2-x)O-4 the Weiss parameter Theta changes with x(Ni), reaching large positive values (e.g., Theta similar to +230 K, for x = 0.5). This phenomenon suggests the existence of a canted-antiferromagnetic or ferrimagnetic structures with large ferromagnetic components. Substitution of cobalt by other 3d or 4d transition metals in the LiMe0.5Co1.5O4 series shows dramatic effects with respect to the non-substituted LiCo2O4 compound: copper completely suppresses the magnetic order, while iron increases T-N to almost room temperature. No modifications are observed when molybdenum substitutes cobalt, while chromium transforms the AF order in a ferromagnetic one, with T-c of about 90 K.