A general mechanism of nonlinear kinetic steps is suggested to account for kinetic instabilities in catalytic oxidation reactions and several isothermal oscillatory models are derived from it. There is still insufficient experimental evidence to construct a detailed model. Physicochemical considerations suggest, however, that the simplest, yet realistic, model should incorporate two surface concentrations as dynamic variables and a slow surface modification such as an oxidation and reduction step. Analysis of the ability of each model to provide efficient communication across the surface shows that the incorporation of thermal and gas-phase concentrations effects is necessary to assure synchronized oscillations. Periodic behavior may emerge in a nonisothermal system with autocatalytic kinetics when its heat capacity is sufficiently large. Coupling of thermal and surface modification effects can lead to complex behavior in the form of multipeak or chaotic oscillations. Periodic behavior can be attributed also to a mechanism incorporating a homogeneous branching and heterogeneous generation steps of a reaction intermediate. Nonlinear kinetics and structure sensitivity are common to oxidation reactions, suggesting a possible relation between these phenomena. Size-dependent kinetics may emerge due to symmetry breaking of the state of a system when surface communication is poor. Apparent structure sensitivity may be observed when a heterogeneous-homogeneous mechanism applies and the active area to catalyst volume ratio is not maintained constant.