The process includes the steps of filling a first reactor (10) with a particulate support (22) comprising a solid matrix to be decontaminated and treated, or a matrix impregnated by a liquid or gaseous matrix to be decontaminated and treated; and introducing at one end (23) of the reactor (10) an oxidative flow triggering a thermoxidation reaction at the opposite end (24) in such a manner that a mobile flame front (26) is generated in the direction opposite (28) to the oxidative flow. The flame front has a temperature of at least 1200.degree. C. so as to substantially decompose or destroy contaminants, undesired substances and compounds initially present in the matrix. Preferably, prior to triggering the thermoxidation reaction, the particulate support (22) is mixed and/or treated with a decontaminating reagent.