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An off-resonance technique, which permits the relaxation rate to be determined as a function of bias field, has been applied to Ni-Fe thin films for the first time. The data provide direct evidence for a strong two-magnon scattering contribution to the losses. The effective linewidth for a 1300-Å film at 9 GHz peaks near the parallel resonance position with Oe. It decreases above and below the ferromagnetic resonance (FMR). is reduced to 60 Oe at a bias 100 Oe below resonance. This sharp falloff indicates that the scattering is due to relatively large inhomogeneities, 3000Å or larger in size. The falloff above resonance is due to a decrease in both the density of states and coupling for the degenerate spin waves. The effective line shift due to spin-wave scattering is also strongly field dependent. It changes by more than 30 Oe in the vicinity of resonance. The data show that line-shift effects should completely obscure ripple field shifts (0.1-1 Oe) which can, in concept, be measured by FMR techniques.