This paper presents an original thermodynamic description of (Mg,Zn)(S,Se) MBE growth, which is in a good quantitative agreement with experimental data. This approach provides large flexibility in choosing different growth regimes of pseudomorphic ZnSe-based heterostructures to obtain desirable alloy composition, surface stoichiometry, and growth rate. The possibility to control a nearly lattice-matched to GaAs composition of a Zn1-xMgxSySe1-y alloy from (x=0, y=0.09) to (x=0.07, y=0.13) only by variation of the Mg flux intensity has been theoretically revealed and experimentally realized in an optically pumped ZnMgSSe/ZnSSe/ZnCdSe SQW SCH laser structure with a threshold power density of 20 kW/cm(2) at 300 K.