The thermoelectric power (S) for a series of RBa 2 Cu 3 O 7Ϫ␦ (RϭY, Gd, Dy) single crystals were measured in the ab plane and along the c direction. The doping level of these crystals changes from highly underdoped (T c ϭ44 K), through optimally doped (T c ϭ90 K) to slightly overdoped (T c ϭ88 K). Both S ab and S c change linearly with the doping level, but S ab reverses its sign near the optimal doping stoichiometry, as it was observed for polycrystalline materials, whereas S c remains positive for the whole series. In contrast to the results of electrical resistivity, the anisotropy of S was found to decrease with both increasing oxygen deficiency and decreasing temperature. A brief overview of thermopower results for single crystals of various high-temperature superconducting families is also presented. ͓S0163-1829͑98͒06102-5͔