  The up-down asymmetry in transversally polarized electron proton scattering
is induced by the interference between one and two photon exchange amplitudes.
Inelastic intermediate hadronic states (different from one-proton state) of the
two photon exchange amplitude give rise to contributions containing the square
of "large logarithm" (logarithm of the ratio of the transferred momentum to the
electron mass). We investigate the presence of such contributions in higher
orders of perturbation theory. The relation with the case of zero transfer
momentum is explicitly given. The mechanism of cancellation of infrared
singularities is discussed.
