Solid solutions in the system zinc sulfide/zinc selenide (ZnS1 -xSex) and in the system zinc oxide/zinc sulfide (ZnO1-xSx) were investigated using the cyclic cluster model within the semiempirical MSINDO method. Results of cyclic cluster calculations for the optimized lattice parameters, band gaps, and binding energies of the perfect zinc chalcogenides ZnO, ZnS, and ZnSe are presented and compared with the experimental data. The miscibility of zinc sulfide and zinc selenide over the complete range of 0 < x < 1 was investigated by calculating the free enthalpy of mixing Delta(M)G for different values of x. The variation of the lattice constant and the band gap in dependence of the composition of the solid solution was determined. The miscibility in the system ZnO1-xSx was investigated for x = 0.02. The free enthalpy of mixing, the variation of the lattice parameters, and the cell volume were calculated. All data are compared with available experimental results.