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Domain wall velocities are measured for 2700 Å and 2200 Å thick Permalloy films of several coercive forces. The velocity-drive field curves are characterized by two mobilities, as often reported. It is found that these low- and high-field mobilities are strongly affected by coercive force of the films. The low-field mobility is nearly constant for low-coercive-force films, and decreases rapidly with increasing coercive force. The high-field mobility is inversely proportional to the coercive force. The measured results suggest that the nonlinear dependence of wall velocity on drive field would disappear in a zero-coercive-force film. None of the mechanisms proposed up to now can explain this behavior of wall velocity in Permalloy films. The nonlinearity is attributed to the transition of material inhomogeneities from pinning centers in low field to dissipation centers in high field.