  We compute the two photon exchange contributions to elastic scattering of
polarized electrons from target protons. We use a nonlocal field theory
formalism for this calculation. The formalism maintains gauge invariance and
provides a systematic procedure for making this calculation. The results depend
on one unknown parameter \bar b. We compute the two photon exchange correction
to the ratio of electric to magnetic form factors extracted using the
polarization transfer experiments. The correction is found to be small if \bar
b ~ 1. However for larger values of \bar b>3, the correction can be quite
significant. The correction to the polarization transfer results goes in the
right direction to explain their difference with the ratio measured by
Rosenbluth separation method. We find that the difference between the two
experimental results can be explained for a wide range of values of the
parameter \bar b. We also find that the corrections due to two photon exchange
depend on the photon longitudinal polarization epsilon. Hence we predict an
epsilon dependence of the form factor ratio extracted using the polarization
transfer technique. Finally we obtain a limit on \bar b by requiring that the
non-linearity in epsilon dependence of the unpolarized reduced cross section is
within experimental errors.
