The single crystalline elastic constants of f.c.c. ferromagnetic Fe-Ni Invar alloys have been determined in both the ferromagnetic and paramagnetic states. The elastic constants reveal pronounced anomalies in the ferromagnetic state which are shown to be closely related to the Invar properties of these alloys. A quantitative description of the Invar behavior of the elastic constants is given in terms of the first and second derivatives of the exchange integral with respect to the interatomic distance. It is shown that a simple and straightforward classification of these effects can be given based on the Bethe-Slater curve. In addition, it is shown that the anomalous behavior of the elastic constant C l —i.e. the anomalously broadened transition from the normal behavior in the paramagnetic state to the anomalous behavior in the ferromagnetic state and the occurrence of a negative ΔE effect in this range—cannot be explained by the Invar properties of these alloys. We have tentatively assumed a structural inhomogeneity which has been subsequently indentified as finely dispersed, coherent precipitates of an ordered phase whose stoichometric composition is presumably Fe 3Ni.