MgSe/CdSe/ZnCdMgSe step quantum well structures and coupled quantum well structures under an applied electric field have been investigated for the process of second harmonic generation (SHG) with the double-resonant condition. The structural parameters of the quantum wells having equally spaced three consecutive energy levels within the conduction band have been determined by solving Schrodinger equation. It is shown that the energy level separation can be continuously tuned between 214 and 472meV by changing the thickness and the material composition of the layers. The product of dipole matrix elements used in determining the second-order nonlinear susceptibility is calculated to be as much as 473 angstrom 3. This is lower than the values obtained in widely known GaAs based material systems because of the high effective mass of electron in these selenides. However, the second-order nonlinear susceptibility 2 that controls SHG is found to be of the order of 10-7 V-1 at its maximum; this is comparable to the values found in similar systems.