Rate oscillations have, been observed in a variety of heterogeneous catalytic reactions including the oxidation of CO. Theoretical studies of these oscillations have involved the application of stability analysis techniques to simplified mathematical models. This dissertation mainly examines isothermal concentration oscillations in the oxidation of dilute CO/alkene mixtures over supported platinum in a stirred tank reactor in the temperature range 90-165°c. The alkenes considered are ethene, propene and 2-butene. Experimental and theoretical considerations are included in this study. The effect of parameters such as temperature, feed flowrate and catalyst loading on these oscillations is investigated. The kinetics of oxidation of CO, propene and ethene are examined in other transient experiments which involve step changes in feed concentration. Comparison of these experiments with the predictions of a mathematical model leads to estimates of the rate constants for CO and alkene oxidation. A modified elementary step ·model (ESM) is proposed to account for the dynamic features of transient experiments. The modification consists of a dependence of the activation energy for alkene desorption from the catalyst on the surface coverage of the alkene. Simulations with unmodified versions of tife ESM and rate constants derived almost completely from .separate transient experiments are shown to lead to stable oscillatory states. A reduced third order model is also shown to predict oscillatory states ·with the same values of rate constants. The effect of periodic changes in the reactor feed concentration on the rate of production of co2 and on the .dynamics of the reaction are also examined. Experimental observations of subharmonic response, a phenomenon predicted but not previously observed experimentally, are reported along with simulations of this phenomenon using the proposed model. This investigation shows that an elementary step model can predict some forms of stable oscillatory states and other dynamic phenomena, and that a modified ESM can predict transient features in the oxidation of CO and alkenes. Further elaboration of the model is needed to predict the range of oscillatory phenomena observed experimentally.