Conventional giant magnetoresistance (GMR) in spin valves is current-independent, so the resistance of a device depends only on the relative orientation of the magnetic layers. In dual spin valves consisting of three ferromagnetic (FM) layers separated by nonmagnetic (NM) spacers (i.e., a FM1/NM/FM2/NM/FM1), GMR can be current-dependent if spin can accumulate in FM2 when outer FM1 layers are aligned antiparallel. Currently the underlying physics is poorly understood, although spin accumulation in FM2 is likely to depend on the gradient in the density of states at the Fermi energy of the ferromagnet. To investigate this hypothesis, we have measured a series of dual spin valves with Ni1-xFex as FM2 layers of varying composition. We show that both the magnitude and sign of the nonlinear GMR depend strongly on the Fe content and thus on the band structure of the ferromagnet FM2.