The steady-state kinetics of enzymes in tissues, cells, and concentrated lysates can be characterized using high-resolution nuclear magnetic resonance spectroscopy; this is possible because almost invariably there are differences in the spectra of substrates and products of a reaction and these spectra are obtainable even from optically opaque samples. We used 1H spin-echo NMR spectroscopy to study the hydrolysis of alpha-L-glutamyl-L-alanine by cytosolic peptidases of lysed human erythrocytes. Nonlinear regression of the integrated Michaelis-Menten expression onto the progress-curve data yielded, directly, estimates of Vmax and Km for the hydrolase; a procedure for analyzing progress curves in this manner was adapted and compared with a commonly used procedure which employs the Newton-Raphson algorithm. We also performed a sensitivity analysis of the integrated Michaelis-Menten expression; this yielded equations that indicate under what conditions estimates of Km and Vmax are most sensitive to variations in experimental observables. Specifically, we showed that the most accurate estimates of the steady-state parameters from analysis of progress curves are obtained when the initial substrate concentration is much greater than Km. Furthermore, estimates of these parameters obtained by such an analysis are most sensitive to data obtained when the reaction is 60-80% complete, having started with the highest practicable initial substrate concentration.