Cavity ring-down spectroscopy is a recently developed technique for highly sensitive detection of atomic and molecular absorptions. Here, we demonstrate the application of this technique to the measurement of kinetics that occur on the same time scale as the loss of light intensity from an optical cavity. We report rate constants for the reactions NO + NO3 --> 2NO(2) and OH + HNO3 --> H2O + NO3 at 296 K, measured as a test of this method. Observed ring-down profiles with a changing absorber concentration match calculated profiles, and fits to these profiles produce rate constants that agree with literature values to within the uncertainty of the measurements. The technique is general and should provide a simple means of measuring kinetic parameters for fast reactions. We also note the possible uses of this method for a variety of kinetics experiments and the outlook for future improvements.