The values of the nonlinear refractive index n2 and the two-photon absorption coefficient β of ternary and quaternary ZnSe-based mixed crystals were extracted from the standard backward degenerate four wave mixing (DFWM) and nonlinear transmission measurements at 532 nm, respectively. Studied crystals were grown by the modified high-pressure Bridgman method. We found that the value of the nonlinear refractive index n2 for Zn0.79Be0.21Se is higher than that for Zn0.80Mg0.20Se. However, the opposite behaviour was found in the case of two-photon absorption coefficient β for these compounds. We also found that the values of the nonlinear refractive index n2 and the two-photon absorption coefficient β for Zn0.83Be0.04Mg0.13Se are about five times lower and three times higher than that for Zn0.80Mg0.13Se, respectively. In the case of ternary ZnSe-based crystals we noticed that the value of the nonlinear refractive index n2 decreases with increasing Mg or Be content. However, the value of the two-photon absorption coefficient β increases with increasing Mg or Be content.