  We present predictions for the value of the cross section ratio $\sigma(e^+p
\to e^+p)/\sigma(e^-p \to e^-p)$, determined from our fit of the elastic $ep$
cross section and polarization data. In this fit we took into account the
phenomenological two-photon exchange dispersive correction.
  The cross section ratios which are expected to be measured by the VEPP-3
experiment are computed. The kinematical region which will be covered by the
E04-116 JLab experiment is also considered. It is shown that for both
experiments the predicted cross section ratios deviate from unity within more
than $3\sigma$.
