Difference Fermi resonance interface modes occur in layered molecular materials when two excitations on one side of an interface differ in energy by an amount that matches approximately the energy of an excitation to which they are coupled on the other side, provided that the mismatch (detuning) is less in magnitude than the non-linear coupling across the interface. Under this resonance condition, the Schr€ o odinger equation is formulated for a superposition of oneparticle and two-particle states, and a set of coupled equations is derived for the allowed energies. The equations are solved for the general cases when there is only one layer on one side of the interface and an arbitrary number on the other side, and also for the case of two layers on either side. Ó