The dual consideration of dye fading phenomena was made an attempt by analysing the adsorption isotherms of substantive dyes in absence of salt. By the proposed analysing method, the fading processes of four kinds of substantive dyes, i. e., Direct Violet 22, Direct Blue 6, Direct Green 6, and Direct Red 28 on cotton and vinylon fabrics, respectively, were discussed, and some chemical factors as a reason for better fastness on vinylon than on cotton, including the dye-fibre bond strength attributed to the different substrate were pointed out. In the present work, the dye-fibre bond strength was expressed as the reciprocal of k$_2$/〔S〕a, where 〔S〕a is concentration in the fibre when all the sites were occupied by monomolecularly adsorbed dye, and k$_2$ is a constant.