A mathematical approach is described for treating stopped-flow spectrophotometric data for very rapid second-order reversible reactions. The treatment involves integration of the theoretical concentration gradient down the length of the observation cell, based on an experimentally measured filling time. No restrictions are placed on the starting reagent concentrations, and allowance is made for the presence ed finite amounts of product at the selected "zero" time, that is, the treatment allows for reversible reactions with prior product formation. Careful calibration of the stopped-flow instrument is required since absolute, rather than relative, values of the absorbance must be utilized. Using a computer analysis based on the described mathematical treatment, it is anticipated that second-order rate constants as large as 10(8) M(-1) s(-1) may be determined with reasonable accuracy for reactions with sizeable absorbance changes (Delta epsilon > 10(4)) using instruments with filling times on the order of 3 ms.