Montmorillonites K-10, Na0.60K0.12Ca0.02(Al1.78Fe0.12Mg0.10)(oct)(Si3.89Al0.11)O-tet(10)(OH)(2) , and NT-25, Na0.10K0.04Ca0.08(Al1.28Fe0.45Mg0.28)(oct)(Si3.94Al0.06)O-tet(10)(OH)(2) , and aluminum oxide, Al2O3, catalyze alkane hydroperoxidation and olefin epoxidation with hydrogen peroxide. Alkanes afford alkyl hydroperoxides as main primary products which partially decompose to produce corresponding ketones and alcohols. The oxidation of cis- and trans-isomers of 1,2-dimethylcyclohexane on K-10 proceeds stereoselectively. Benzene in the presence of montmorillonite K-10 is transformed into phenol. Styrene is oxidized to afford benzaldehyde and styrene epoxide. It is proposed on the basis of a kinetic study and measurements of the selectivity parameters that in the case of alumina the oxidation occurs with the participation of hydroxyl radicals generated from an aluminum peroxo derivative on the catalyst surface. In the cases of montmorillonites iron centers are also responsible for the H2O2 activation which gives hydroxyl radicals. Addition of trifluoroacetic acid (TFA) leads to the noticeable acceleration of all oxidation reactions and enhancement of the product yield. It has been shown that in the presence of TFA some parts of solid catalysts are transferred into the homogeneous solution. Thus, very cheap natural solid materials provide soluble species that are active in efficient homogeneous oxidations of hydrocarbons with hydrogen peroxide. In the absence of TFA the oxidation reactions in the case of the three catalysts are truly heterogeneous in nature.