Catalytic wet-air oxidation (CWAO) of wastewater (chemical oxygen demand [COD] = 1800 mg O2/dm3) from a fine chemicals plant was investigated in a fixed-bed reactor at T = 393-473 K under total pressure of 5.0 or 8.0 MPa. Catalysts containing 0.3% wt. of platinum deposited on two supports, mixed silica-titania (SM1) and carbon black composites (CBC) were used. The CBC-supported catalyst appeared to be more active than the SM1-supported one. A slow decrease of activity of the platinum on SM1 (Pt-SM1) during the long-term operation is attributed to recrystallization of titania and leaching of a support component, while the Pt-CBC catalyst is deteriorated, owing to combustion of the support component. The power-law-kinetic equations were used to describe the rate of COD removal at CWAO over the catalysts. The kinetic parameters of COD reduction for the wastewater were determined and compared with the kinetic parameters describing phenol oxidation over the same catalysts. Rates of COD removal for the wastewater were found higher than those for phenol oxidation over the same catalysts and under identical operating conditions.