  We estimate the two-photon exchange contribution to elastic electron-proton
scattering at large momentum transfer $Q^2$. It is shown that the leading
two-photon exchange amplitude behaves as $1/Q^4$ relative to the one-photon
amplitude, and can be expressed in a model independent way in terms of the
leading twist nucleon distribution amplitudes. Using several models for the
nucleon distribution amplitudes, we provide estimates for existing data and for
ongoing experiments.
