Add to ORKGLinear and nonlinear processes of transferring optical singularities from anisotropic crystals onto the wavefront of Bessel light beams (BLBs) are investigated. The generation of high-order vortices at the propagation of BLBs along the optical axes of crystals was studied. Particularly, a nonlinear frequency doubling of Bessel vortices in the conditions of new type synchronism (full conical phase-matching) is considered. This scheme of three-wave interactions of BLBs based on that the spatial frequency cones of BLBs coincide with phase-matching cones of uniaxial crystals. New type of frequency doubling of Bessel vortices has been experimentally realized in uniaxial crystals