Recently, new of classes multi-component Rare Earth (R) - Transition Metal (T)-compounds with high melting temperatures (> 1500°C) have been discovered. Since 1994 intermetallic R-T-borocarbides, RT2B2C (R = rare earth elements, Sc, Y, or La; T = Ni, Pd), have attracted much attention because of superconducting transition temperatures as high as TC = 23 K and the interplay of superconductivity and magnetic ordering. The RNi2B2C intermetallic compounds exhibit the tetragonal body-centered ThCr2Si2-type crystallographic structure. Single crystals grown by the Ni2B-flux method provide a basis for determination of several anisotropic physical properties. However, they suffer from relatively small size and imperfections arising from the flux. Therefore, single crystals of HoNi2B2C and YNi2B2C with dimensions 6 mm in diameter and 30–50 mm in length have been grown by floating zone technique with optical heating. Crystals are crack free, show no traces of 2nd phase and are single crystalline in the whole volume with a neutron rocking curve half-width less than 0.45°. To optimize the crystal perfection the crystals were annealed in a two step procedure at 1000°C for 72 h and at 500°C for another 72 h. The superconducting properties show the best characteristics reported up to now. The YNi2B2C crystals are characterized by a superconducting transition temperature Tc of 15.6 K with a width of ΔTc= 0.1 K and a residual resistivity ratio of RRR = ρ300 K/ρ16 K = 61. Single crystals of HoNi2B2C after annealing show a transition temperature Tc of 8.5 K and a residual resistivity ratio of RRR = ρ300 K/ρ9 K = 18.figure