The magnetic excitation spectra of Kondo insulators, is examined in the vicinity of a magnetic transition. The Kondo insulators are modeled by the Anderson Lattice Hamiltonian, which has a hybridization gap between the bands in the quasi-particle dispersion relations. At precisely half-filling, the system becomes an indirect gap semiconductor. The spectrum of magnetic excitations contains contributions from spin-flip electron-hole excitations which form a continuum above a threshold energy, and a contribution from collective excitations. The spectrum of collective excitations softens at the magnetic instability. For ferromagnetic systems, the magnetic instability is accompanied by an exchange splitting which if sufficiently large can drive the system from the insulating state to a metallic state. The theory is applied to UNiSn. (C) 1998 Published by Elsevier Science B.V. All rights reserved.