A component distribution in Ge-rich Ge-Si single crystals grown under the continuous feeding of the melt with the second component (Si) has been analyzed theoretically and investigated experimentally with a view to establish the operational parameters and optimum processing conditions in preparing bulk crystals with a desired uniform and/or graded composition profiles. It was found that a numerical model can be successfully applied for estimating the macroscopic axial composition profiles in Ge-rich Ge-Si single crystals. A modified double crucible method was developed to grow graded and uniform Ge-Si bulk single crystals using the continuous feeding of the melt with a Si rod. The method for the growth of compositionally graded and uniform Ge-Si bulk single crystals from a starting pure Ge melt using a Ge seed followed with continuous feeding of the melt with a Si rod was used and considered. Two stages of the feeding rate of the melt were developed to increase a uniform portion of the crystals grown by this method. We were successful in growing compositionally graded and uniform Ge-Si single crystals with Si content up to 15 at% using theoretically established operational parameters (growth and feeding rates: a starting melt composition). The length and diameter of the crystals are 30-70 and 5-9 mm, respectively.