We report on the status of the Novosibirsk experiment on a precision measurement of the ratio $R$ of the elastic $e^+ p$ and $e^- p$ scattering cross sections. Such measurements determine the two-photon exchange effect in elastic electron-proton scattering. The experiment is conducted at the VEPP-3 storage ring using a hydrogen internal gas target. The ratio $R$ is measured with a beam energy of 1.6 GeV (electron/positron scattering angles are $theta = 55 div 75^{circ}$ and $theta = 15 div 25^{circ}$) and 1 GeV ($theta = 65 div 105^{circ}$). We briefly describe the experimental method, paying special attention to the radiative corrections. Some preliminary results are presented.
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