A detailed kinetic study on the deep oxidation of propane was carried out in a wide range of temperatures and concentrations using a novel Pt-fiberglass catalyst. Highly dispersed 1-1.5 nm Pt2+-Pt-0 metal-oxide clusters are confined in the bulk of glass at a depth up to 20 nm. In spite of extremely low platinum content (0.01-0.02%), this catalyst showed a very high activity in the propane oxidation. The modified Langmuir-Hinshelwood mechanism including reversible adsorption of molecular oxygen and irreversible adsorption of propane and its subsequent combustion by adjacent oxygens was proposed. The simplest kinetic model adequately describing such experimental features like the extremal dependence of the reaction rate on the O-2 concentrations, the sharp changes of reaction order with respect to oxygen, the significant growth of apparent activation energy with decreasing the oxygen concentration, etc. was developed. In particular, the extremal dependence is caused by competitive adsorption of propane and oxygen on the different active sites. At high O-2 concentrations, the adsorbed oxygen occupies virtually all active sites that are accessible for propane adsorption, and the reaction rate sharply decreases. In the case of oxygen deficiency, the adsorbed propane does not occupy completely the active sites for oxygen adsorption, so that the reaction rate increases with propane concentration. The maximum reaction rate is attained at the defined O-2/C3H8 ratios when the concentrations of adsorbed oxygen and propane are comparable.