We investigate the categorization of two or more proposed reaction mechanisms for each of the following oscillatory enzymatic reactions : (1) the peroxidase-oxidase reaction; (2) glycolytic oscillations; (3) oscillations of cyclic AMP in slime mold cells; (4) enzymatic pH oscillations; (5) calcium spiking in cytosol. We use prior work in stoichiometric network analysis and categorization of oscillatory reactions to identify in each proposed reaction mechanism essential and nonessential species, the specific role of each essential species, the connectivity of the essential species, including the identification of the reactions leading to oscillatory instabilities, and the category. For each model, we predict the results of several experiments including relative amplitudes, quench amplitudes, phase shifts, and sign symbolic concentration shifts and compare them with those from available experiments. These and several other experiments such as bifurcation analysis,phase response curves, entrainment experiments, qualitative and quantitative pulsed species response, delay experiments, and external periodic perturbation provide stringent tests of proposed reaction mechanisms, and appropriate ones are suggested to discriminate among competing mechanisms for a given reaction. We find the necessity for introducing a new subcategory in our categorization of oscillatory reactions. The details of the analysis for reactions 2-5 and of the methods determining the categories are given in the Supporting Information.