Electrocatalytic oxidation of two anti-inflammatory drugs (Mefenamic acid and Indomethacin) was investigated on a cobalt hydroxide modified glassy carbon (CHM-GC) electrode in alkaline solution. The process of oxidation and its kinetics were established by using cyclic voltammetry and chronoamperometry techniques as well as steady state polarization measurements. Voltammetric studies indicated that in the presence of under study drugs, the anodic peak current of low-valence cobalt species increased, followed by a decrease in the corresponding cathodic current. This result indicates that the drugs were oxidized via cobalt hydroxide species immobilized on the electrode surface via an E$acute{C}$ mechanism. A mechanism based on the electrochemical generation of Co (IV) active sites and their subsequent consumption by the drugs in question was also investigated. The constants rate of the catalytic oxidation of the drugs and the electron-transfer coefficients reported.