The present invention is a process to oxidize a contaminant in a permeable subterranean formation by introducing an aqueous treating solution into the formation which solution contains hydrogen peroxide and a compound to control the mobility of the aqueous solution by increasing the viscosity, the density, or modifying the interfacial properties of the aqueous solution within the formation. The aqueous treating solution may also contain stabilizers for the hydrogen peroxide, free radical initiators, or free radical traps. Optionally, the formation may be pretreated to modify the permeability of the formation, to deactivate or remove hydrogen peroxide decomposition catalyst or to uniformly distribute free radical initiators therein.