Giant magnetoresistance (GMR) arises from differential scattering of the majority and minority spin electrons by a ferromagnet (FM) so that the resistance of a heterostructure depends on the relative magnetic orientation of the FM layers within it separated by nonmagnetic spacers. Here, we show that highly nonequilibrium spin accumulation in metallic heterostructures results in a current-dependent nonlinear GMR which is not predicted within the present understanding of GMR. The behavior can be explained by allowing the scattering asymmetries in an ultrathin FM layer to be current dependent.