dc magnetization measurements in fields up to 5 T on single crystals of YBa2Cu3C>7-5 reveal a well defined onset of diamagnetism allowing a unique magnetic determination of the upper critical field and its anisotropy. The upper-critical-field slopes are -1.9 and -10.5 T/K corresponding to coherence lengths of 16 and 3 A for fields perpendicular and parallel to the Cu-O planes. At the magnetically determined nucleation temperatures no distinct features are found in resistive transition curves.PACS numbers: 74.70.Vy, 74.60.EcThe values of the upper critical fields H C 2 in the high-TV superconductors are important quantities since they give the most direct information about microscopic parameters like the superconducting coherence lengths and their anisotropics within the superconducting state. So far H C 2 of YBa2Cu307-5 and other high-TV materials has been determined mainly from resistive transition curves. 1,2 However, this is complicated by an unusual broadening of the transition in a magnetic field. This behavior has been attributed to flux motion 3 ' 4 or the field dependence of the critical current in a network of Josephson junctions. 5 The flux-flow interpretation has been supported by the observation of a frequency dependence 6 of the apparent H C 2 determined by highfrequency inductive measurements and by the observation of flux creep in dc magnetization measurements. 7 These interpretations imply that resistive measurements of H C 2 yield values that are significantly lower than the equilibrium values.In order to address these issues we have carried out resistive and magnetic measurements of H c i on highquality single crystals of YBa2Cu307-5. We observe that the magnetization in a temperature interval of about 8 K ( depending on the applied field) below T c is reversible and linear in temperature, the behavior expected from 3D Ginzburg-Landau (GL) theory. Therefore these measurements reflect an equilibrium state and are not complicated by effects due to flux motion. In contrast to resistivity measurements, dc magnetization measurements in an applied field show a well defined onset of diamagnetism which allows a unique determination of the critical field. Values of H C 2 and the critical-field slopes determined in this way are considerably larger than those determined resistively. From the magnetic measurements of H C 2 we derive the superconducting parameters and the jump in the specific heat at T c which agrees well with reported experimental results. 8 Single crystals of YBa2Cu307-5 were prepared by a partial melting method. 9 Many crystals are produced in a single batch process and exhibit sharp transitions at T c > 92 K. Samples have the shape of plates with dimensions of about 0.2x2x3 mm 3 . They display patterns of twin boundaries with mm spacing which are visible with a light microscope. dc magnetization was measured with a commercial SQUID magnetometer in fields up to 5 T. In addition, magnetization measurements below 50 Oe were performed in a low-field SQUID magnetometer, ac resistivity and mag...