We discuss whether the behaviour of some hadronic quantities, such as the
total cross-section, the ratio of the elastic to the total cross-section, are
presently exhibiting the asymptotic behaviour expected at very large energies.
We find phenomenological evidence that at LHC7 there is still space for further
evolution.Comment: 5 pages, 2 figures, talk given by G. Pancheri at International
Workshop on Diffraction in High-Energy Physics, DIFFRACTION 2012, Puerto del
Carmen, Canary Islands, Spain. To appear in AIP Conf. Pro