- As a whole new range of energies will be soon experimentally studied, we present predictions for hadronic cross sections at future very high energy accelerators. All calculations are based on results accumulated in reggeon field theory, where methods of field theory (in the continuum and on the lattice) and statistical mechanics have been used. We have employed these results and translated them into a manageable phenomenological analysis of existing FERMILAB-ISR data. The size of the non-leading terms is determined and enables us to predict cross sections at energies in the range of the near futurep¯p collider. Parameter-free scaling functions and critical exponents which are exactly calculable in RFT are thus brought to an experimental test.