The objective of this work is to understand the role of physicochemical properties of LaCoO3-CeO2-Co3O4 system with particular attention to the importance of phase segregation. The catalytic materials used were all prepared by the citrate method. They comprised: (i) single phase simple oxides and perovskites; (ii) in situ formed multiphase oxides of nominal compositions La1-xCexCoO3 (x = 0-0.5) prepared from a single solution precursor: (iii) lanthanum-cobalt mixed oxides impregnated with ceria by using cerium trinitrate; and (iv) mechanical mixtures of LaCoO3, CeO2 and Co3O4. Most of the materials were characterized by several methods (XRD, XPS, TPD-O-2). The activity of all of them was determined under the same conditions, using 0.1 g catalyst, 1% methane in air at a flowrate of 75 ml/min. Partial replacement of lanthanum by cerium in LaCoO3 results in a significant improvement of activity, which can only partially be explained by the formation of a defective, perovskite related structure permitting higher oxygen mobility. In La1-xCexCoO3 compositions with x > 0.05, segregation of ceria and other phases occurs. The corresponding high activity seems to result from cooperation between the phases. Some phase cooperation appears to occur even in the mechanically blended mixtures of LaCoO3-CeO2-Co3O4. While phase cooperation is well known in the case of partial oxidation catalysts, it had not been yet explicitly proposed as such in the case of total oxidation (combustion) catalysis.