A Green's function technique is used to study the spin dynamics in the Invar alloys. The longitudinal dynamical structure factor has been calculated. It exhibits a three-peak structure: two peaks due to magnetovolume interactions and a central peak due to the coupling of the transverse mode and the longitudinal relaxing mode. The dependence of the three peaks on temperature T, wave vector k, magnetic field H, and Ni concentration is discussed. The results are in good agreement with the experimental data for the Fe-Ni Invar alloys.