A catalyst for the full oxidation of volatile organic compounds (VOC), particularly hydrocarbons, and of CO to CO2, comprising: a non-stoichiometric crystalline compound conventionally designated by a formula which corresponds to A14Cu24O41 (I), where A is Sr or a solid solution of Sr with alkaline-earth metals, alkaline metals, lanthanides; or a non-stoichiometric crystalline compound conventionally designated by a formula which corresponds to B4Cu5O10 (II), where B is Ca or a solid solution of Ca with alkaline-earth metals, alkaline metals, lanthanides; or mixtures thereof; and in that it is prepared in a form which has a large specific surface area, preferably larger than 25 m2/g; a method for preparing the catalysts; their use in methods for the full oxidation of VOC and of CO to CO2; and the oxidation methods.