The energies of long-wavelength spin waves in iron-nickel alloys have been measured as a function of composition, using a neutron small-angle scattering technique. The behaviour of the composition dependence can be explained in terms of a simple model invoking long-range interaction functions J(r) between the three different types of atom pair, Fe-Fe, Fe-Ni, and Ni-Ni. There is evidence that on the body-centred cubic lattice the iron-nickel interaction J(r) changes sign from positive to negative as a function of distance. Between Fe-Fe pairs on a face-centred cubic lattice, the `exchange integral' as normally defined is found to be -9 ± 2.6 mev, which is consistent with other indications that face-centred cubic iron is antiferromagnetic.