The real and imaginary parts of the complex permeability have been measured for a series of iron-nickel alloys in the frequency range 300-400 Mc/s. The frequency of the internal resonance observable in this region has been investigated as a function of composition and is found to pass through a minimum in the neighbourhood of 70% Ni. The value of the principal anisotropy coefficient is also known to be very small in this region and a qualitative comparison provides additional support for the view that this resonance is attributable to the equivalent magnetic field associated with the anisotropy energy.