CdTe crystals doped with dysprosium were grown by the vertical Bridgman method to explore the possibility of obtaining Cd1−xDyxTe ternary compound. The growth was carried out from the Cd1−xDyxTe pre-synthesized feeds with the charge composition in the range of x=0.001–0.05. The as-grown crystals were studied by scanning electron microscopy, X-ray diffraction and optical spectroscopy. Experimental findings testify that the Cd1−xDyxTe crystals have the homogeneous cubic structure similar to CdTe in the narrow composition range of x≈0–0.01. At higher compositions x≥0.01, the crystals become a mixture of several phases such as CdTe host, Dy2Te3 textures and DyTe-rich inclusions.