  At very high energies we expect that the hadronic cross sections satisfy the
Froissart bound, which is a well-established property of the strong
interactions. In this energy regime we also expect the formation of the Color
Glass Condensate, characterized by gluon saturation and a typical momentum
scale: the saturation scale $Q_s$. In this paper we show that if a saturation
window exists between the nonperturbative and perturbative regimes of Quantum
Chromodynamics (QCD), the total cross sections satisfy the Froissart bound.
Furthermore, we show that our approach allows us to describe the high energy
experimental data on $pp/p\bar{p}$ total cross sections.
