Asymptotic hadron scattering regimes in QCD

We discuss possible modes of the asymptotic behavior of hadron scattering amplitudes in QCD. We show that the triviality condition for the scattering matrix with the interaction of the fundamental fields turned off leads to the impossibility of cross sections nondecreasing with energy in the case of pure gluodynamics. We also show that this ban is lifted in the presence of at least one type of massive quark. We also discuss some consequences of the presence of an infrared fixed point.