A method is described to obtain reaction rates of chemical reactions in a network in which there are more independent reactions thatn independent chemical species. The method makes use of the linear theory of nonequilibrium thermodynamics to obtain the equilibrium exchange rates of the reactions, which are calculated from the relaxation data as the system approaches chemical equilibrium. A method which follows very closely that of Wei and Prater (1962) can be used to treat the relaxation data. As an example, the method was applied to the methanol synthesis reaction from CO, CO2, and H2 over a Cu-Zn oxide catalyst. It was concluded that successful application of the method is limited to systems in which all the processes contributing to the observed relaxation are known, in addition to the common limitations due to noise in experimental measurements.