Using a combination of first-principles molecular dynamics and conventional electronic-structure calculational methods, we examine the pronounced bowing phenomenon, which characterizes the direct energy gap EΓg in ZnSe1-xTex alloys. The bowing of EΓg is found to be attributable to significant electronegativity difference between the two anions. We also examine the structure of sinusoidally modulated ZnSe1-xTex superlattices whose composition varies in the range of 0.25<x<0.75. We find an elongation of the Zn-Te bond and a contraction of the Zn-Se bond relative to those of the corresponding binary compounds. The elongation of the Zn-Te bond may explain the redshifts of EΓg of 0.14 eV observed in the photoluminescence measurements on these supperlattices. We also study the electronic and structural properties of the Zn1-xBexSe and Zn1-xCdxSe alloys and find that in the Zn1-xBexSe alloys the Zn-Se bond length decreases slightly, while the Be-Se bond length increases by 10% relative to those of the binary compounds. This result suggests a softening of the Be-Se bond in the Zn1-xBexSe alloys. For Zn1-xCdxSe, the Zn-Se and Cd-Se bond lengths deviate from those of the respective binary compounds by not more than 2%. We also find that the direct band gap EΓg as a function of x bows down for both Zn1-xBexSe and Zn1-xCdxSe in agreement with experimental data.