Abstract:We show how to obtain the leading energy dependence of hadronic total cross sections, in the framework of the nonperturbative approach to soft high-energy scattering based on Wilson-loop correlation functions, if certain nontrivial analyticity assumptions are satisfied. The total cross sections turn out to be of "Froissart" type, σfor s → ∞. We also discuss under which conditions the coefficient B is universal, i.e., independent of the hadrons involved in the scattering process. In the most natural scenarios for universality, B can be related to the stable spectrum of QCD, and is predicted to be B th 0.22 mb, in fair agreement with experimental results. If we consider, instead, the stable spectrum of the quenched (i.e., pure-gauge) theory, we obtain a quite larger value B (Q) th ≥ 0.42 mb, suggesting (quite surprisingly) large unquenching effects due to the sea quarks.