A biosorbent prepared from moss Rhytidiadelphus squarrosus biomass was used for biosorption of cationic dyes – Malachite green (BG4), Auramine O (BY2) and Thioflavine T (BY1) from binary aqueous solutions. Sorption data obtained at non-equilibrium conditions were analyzed by Sheindorf-Rebuhn-Sheintuch (SRS) equation (competitive model for binary systems derived from Freundlich isotherm) and extended model of Freundlich isotherm. Following the comparison of coefficient of determination values (R2) as well as values of root mean squared error (RMSE), the extended model of Freundlich isotherm was more suitable for description of investigated binary systems BG4-BY1 (R2 BG4 = 0.983, R2 BY1 = 0.993) and BG4-BY2 (R2 BG4 = 0.976, R2 BY2 = 0.995). The competition coefficients aij, obtained from SRS model can be considered as a way to quantify mutual competitive interactions. The competition coefficients indicated that the presence of BY1 in binary system decreased the sorption of BG4 (aBY1,BG4 = 0.835) while presence of BG4 (aBG4,BY1 = 0.208) has less pronounced competitive effect on the sorption of BY1 onto biosorbent. Competition coefficients obtained for binary system BY1-BG4 indicate that BG4 (aBG4,BY2 = 0.186) was more significantly affected by the presence of BY2 (aBY2,BG4 = 1.167). Finally, equations used in this work were represented by the three-imensional biosorption isotherm surfaces.