A new approach for the determination of the amyloid fibril - thioflavin T (ThT) binding parameters (the number of binding modes, stoichiometry, and binding constants of each mode) is proposed. This approach is based on the absorption spectroscopy determination of the concentration of free and bound to fibril dye in solutions, which are prepared by equilibrium microdialysis. Furthermore, the proposed approach allowed us, for the first time, to determine the absorption spectrum, molar extinction coefficient, and fluorescence quantum yield of the ThT bound to fibril by each binding modes. This approach is universal and can be used for determining the binding parameters of any dye interaction with a receptor, such as ANS binding to proteins in the molten globule state or to protein amorphous aggregates.