Two dimensional models for hydrodynamic systems, such as soap films, have been studied for hundreds of years. Yet there has not existed a fully nonlinear system of dynamic equations analogous to the classical Euler equations. We propose an exact nonlinear system for the dynamics of a fluid film. The system is derived in the classical Hamiltonian framework and neither the velocities nor the deviation from the equilibrium are assumed small. We discuss the properties of the proposed equations and results of numerical simulations.