An experimental study of kinetics of peptide binding to MHC proteins [S. Witt, H. McConnell, Acc. Chem. Res. 26 (1993) 442 (and references therein)] showed an unusual phenomenon of the so-called 'negative' t1/2 plots (where t1/2 is half time of reaching equilibrium concentration of peptide-protein complexes), which is the shorter t1/2 at lower added peptide concentrations. The bell-shaped curve for t1/2 as a function of peptide concentration is a seemingly peculiar effect, because in general, binding reactions go faster with an increase of reagent concentrations. It is shown that the suggested explanation of this phenomenon [S. Witt, H. McConnell, Acc. Chem. Res. 26 (1993) 442 (and references therein)] is misleading (and the numerical simulation used to support this explanation is inconsistent with the experimental data), so that the existence of 'negative' t1/2 is in no way to be considered as an experimental indication of the two-step reaction of peptide binding to protein. This article gives a consistent explanation of the bell-shaped t1/2 plots for peptide-protein association and obtains the criteria for its existence, based exclusively on the formal chemical kinetics analysis of the accepted peptide-protein binding model and briefly discusses the experimental data, which really confirm the existence of the two-step mechanism of binding. The analysis of the maximum location of the half-time curves indicates a controversy between the prediction of the two-step binding model and the experimental data [S. Witt, H. McConnell, Acc. Chem. Res. 26 (1993) 442 (and references therein)]: either more complicated mechanism is involved in peptide-MHC binding or experimental data [S. Witt, H. McConnell, Acc. Chem. Res. 26 (1993) 442 (and references therein)] are not quite accurate.