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A model for both proton and photon total cross-sections is presented andcompared with data. The model is based on the eikonal representation, with QCDmini-jets to drive the rise and soft gluon kt-resummation into the Infraredregion to tame the excessive rise due to low-x perturbative gluons. We discussthe effects of a singular but integrable expression for the Infrared gluonspectrum on the high energy behaviour of the total cross-section expected inthis model.

Total Cross-sections at very high energies: from protons to photons