The Hall electric field E y is observed to be a strongly nonlinear function of the current density J x in the vicinity of the vortex-glass transition of YBa2Cu307-«5 films in a magnetic field. Much like the longitudinal electric field E x , E y appears to scale critically with J x , with a Hall-related critical exponent A = 3.4 ± 0.3. Furthermore, the Hall resistivity p xy -E y /J x and the longitudinal resistivity p xx = E x /J x are found to obey p xy oc p xx ±0 ' 2 over a wide range of current densities and temperatures. The results quantitatively verify recent theoretical predictions.PACS numbers: 74.60. Ge, 73.50.Jt, 74.76.Bz In this Letter, we report on the first observation of nonlinear Hall resistivity in YE^CusOr-^ films in the vicinity of the vortex-glass transition in a high magnetic field, i.e., the Hall electric field E y is a nonlinear function of the driving longitudinal current density J x . At the vortex-glass transition temperature T g , YE^CusOy-s films pass from a vortex liquid to a vortex glass state [1]. As it appears, the Hall resistivity becomes increasingly of nonlinear character upon approaching T g from above, and turns entirely nonlinear below T g .Entering the nonlinear regime implies, as quite general arguments show [1], that the length scales on which the system is probed becomes of the order of the vortex-glass correlation length, which diverges at T g . It therefore puts theories of the Hall effect relying on vortex dynamics to a particularly severe test. This, in fact, is the objective of this Letter. Contrary to the nonlinear Hall effect, the linear Hall effect, which is only observed at sufficient distance from the transition and at sufficiently low currents, has recently attracted considerable attention. The focus of the interest has been on the intriguing sign change that occurs upon cooling from the normal to the vortex liquid state [2][3][4][5][6][7][8]. Of particular relevance here furthermore is the finding by Luo et al. [9] that in the linear regime the Hall resistivity p xy -E y /J x as a function of the temperature follows a power-law dependence on the longitudinal resistivityTwo theories are available for the Hall effect in superconductors in the nonlinear regime. First, inspired by the results of Luo et al [9], Dorsey and Fisher (DF) [10] devised a critical scaling model, elaborating on the fact that the Hall effect in superconductors is an expression of the particle-hole asymmetry. In the vicinity of the vortexglass phase transition [1], this asymmetry is assumed to scale with a power of the vortex-glass correlation length. The linear Hall resistivity then exhibits a critical scaling behavior, in consistency with experiment [9], Furthermore, DF made an explicit prediction for the Hall effect, which may serve as an independent test of their theory: "The nonlinear Hall electric field E y should exhibit universal scaling, and right at the transition should vanish with a universal power of the current density J x ." An alternative, but not necessarily incompatible, ...