AlN crystals have been grown by the sublimation technique on the various seeds in the conventional growth system designed earlier for SiC ingot growth by modified Lely method. Phase composition and structure of AlN deposits were determined by X-ray diffraction methods (double-crystal diffractometry, Laue patterning, rotation technique etc.). Growth of AlN single phase crystalline deposits onto the single crystalline SiC substrates is impeded due to formation of complex carbides such as Al4SiC4 and Al4Si2C5 at the growth interface. Single crystalline growth has been achieved onto AlN/Al2O3 epitaxial structures at the temperatures less than 1800degreesC. The deposit with thickness of up to some millimeters has been grown onto the substrate of up to 1 inch in diameter. X-ray diffraction showed that this deposit had wurtzite structure typical for AlN. Lattice parameters were agreed with the tabulated.