The flux-flow Hall conductivity o;Y in untwinned YBa2Cu30693 (YBCO) is determined from Hall and resistivity measurements with the current applied along the a and the b axes. We show that sign reversal results from competition between a positive quasiparticle current (-H) and a negative vortex-motion term ( -1/H) The H. all drag coefficient in YBCO is measured to be a(T)= -4.4X10 (1 -T/T, ) Ns/m (75&T&93 K). In single-crystal La@ Sr,Cu04, a similar decomposition into quasiparticle and vortex currents (both positive) is possible even though o;~s hows no sign reversal. The behavior of the Aux-flow Hall effect in high-T, superconductors is a challenging problem in the rich phenomenology of vortex dynamics in type-II superconductors. Of particular interest is the sign reversal observed in the Hall resistivity pyx of most of the cuprates. ' Many models have been proposed to explain this anomaly. However, until recently, the crucial contribution of quasiparticle excitations to the observed current has not been appreciated. Dorsey and Kopnin, Ivlev, and Kalatsky independently proposed that the sign reversal could arise if the quasiparticle and vortex Hall currents have opposite signs. Because of the additivity of the two currents, the simplest way to express the quasiparticle contribution is by the conductivity, viz. , n xy xyw here o;y is the total conductivity and o;" (cr, ) is the Hall conductivity of the quasiparticles (vortices). Following a suggestion by Geshkenbein and Larkin (GL), Harris, Ong, and Yan (HOY) extracted the Hall conductivity of YBa2Cu306 93 (YBCO) measured in oblique fields and found striking agreement with the scaling relationship of GL. Further, HOY found that the vortex term tr" is negative at all fields and tilt angles. The additivity in Eq. (1) has also been tested by Samoilov, Ivanov, and Johans son in T12Ba2CaCu208+ &, and by Ginsberg and Manson on untwinned YBCO crystals. Harris et al. ' reported that, in highpurity 60-K YBCO crystals, oxy is negative below 40 K at all fields 0 up to -24 T with a field dependence that approaches -1/H at high fields. These experiments show that the sign reversal is a direct consequence of adding a positive term that increases with 0 to a negative term that varies as -1/H. A different analysis, based on additivity of the Hall angles, has been proposed by Kunchur et al. We report Hall measurements on two untwinned crystals of YBCO and a crystal of La2, Sr"Cu04 (LSCO). In YBCO, the ratio of the resistivities p"and pb, measured with JIIa and J~Ib, respectively, varies strongly with H and T in the mixed state. (J is the current density; H~~c in all measurements. ) To determine the Hall conductivity o. ,b, it is necessary to measure both p"and pb. We selected two untwinned, optimally doped YBazCu30693 crystals (A and B) with closely similar electrical properties (caption of Fig. 1). The Hall resistivity pb, (p, b) and the resistivity p, (pb) were measured simultaneously in crystal A (B). The four quantities allow the Hall conductivity o. y -= o. ,b to be calculated...