  We consider the possible contribution of Odderon (Reggeon with alpha_(Odd)(0)
similar to 1 and negative signature) exchange to the differences in the total
cross sections of particle and antiparticle, to the ratios of real/imaginary
parts of the elastic pp amplitude, and to the differences in the inclusive
spectra of particle and antiparticle in the central region. The experimental
differences in total cross sections of particle and antiparticle are compatible
with the existence of the Odderon component but such a large Odderon
contribution seems to be inconsistent with the values of Re/Im ratios. In the
case of inclusive particle and antiparticle production the current energies
and/or accuracy of the experimental data don't allow a clear conclusion. It is
expected that the LHC will finally solve the question of the Odderon existence.
