We discuss the nonlinear dynamics of an interface between two layers of organic semiconductors in the case of a Fermi resonance which occurs when the energy (h) over bar omega(c) of excitation on one side of the interface is approximately equal to 2 (h) over bar omega(b) with (h) over bar omega(b) being the excitation energy on the other side. We develop the theory of quantum Fermi resonance interface modes (FRIM) propagating along the interface and demonstrate that the Fermi resonance interaction across the interface also gives rise to classical nonlinear plane waves propagating along the interface and in some cases to 2D solitons localized at the interface.