  We study soft gluon kt-resummation and the relevance of zero momentum gluons
for the energy dependence of total hadronic cross-sections. We discuss a model
in which consistency of the energy dependence of the cross-section with the
limitation of the Froissart bound, is directly related to the behaviour of the
strong coupling constant in the infrared region. Our predictions for the
asymptotic behaviour are shown to be related to the ansatz that the infrared
behaviour of the QCD strong coupling constant follows an inverse power law.
