High-energy total cross sections on nuclei

We discuss some features of the description of hadron-nucleus total and inelastic cross sections at present and foreseeable energies within the framework of Reggeon calculus. In the first (theoretical) part we discuss the Amati-Stanghellini-Fubini cancellation, emphasizing the analytic features involved, especially the consistency with unitarity in the Reggeon-particle channel. In the second (phenomenological) part we show that the observed triple-Pomeron coupling is so small that effects of Reggeon interactions can probably be ignored both at Fermilab energies and for observations of extensive air showers. It follows that the Glauber formula should describe all current experiments with only small corrections for inelastic intermediate states