To settle the question whether the growth with energy is universal for different hadronic total cross-sections, we present results from theoretical models for pion-proton, proton-proton and proton-antiproton total cross-sections. We show that present
and planned experiments at LHC can differentiate between different models, all of which are consistent with presently available (lower energy) data. This study is also relevant for the analysis of those very high energy cosmic ray data which require reliable pion-proton total cross-sections as seeds. A preliminary study of the total pion-pion cross-sections is also made.
