We report on the growth and basic characterization of new quantum well structures made of diluted magnetic semiconductors. The novelty of the structures has two aspects. First, by molecular beam epitaxy we attempted to grow diluted magnetic semiconductor materials containing chromium ions as the magnetic component. We succeeded in obtaining materials containing up to 3 atomic percent of Cr in ZnTe and CdTe hosts. The structural quality of these materials grown in a form of relatively thick (1-4 mu m) epitaxial layers, as evidenced by X-ray double rocking curves, degrades quickly with an increasing molar fraction of Cr. The lattice parameter of the cubic, zinc-blende phase is found to increase with the Cr contents. On the other hand, the optical quality of the structures containing Cr ions only in the quantum wells regions is quite satisfactory. The second aspect of the novelty of the reported structures is related to a precise composition profiling. The digital growth method in MBE is used to fabricate parabolic, half-parabolic and triangular quantum wells. Such structures are more effective in confining electron and hole motions than the usual rectangular quantum wells, as evidenced by large exciton binding energy values.