  Several models of minimum-bias hadronic interactions at ultra-high energy
that have been used for calculations of air showers share essential common
features. In this talk I review these common elements and discuss some
consequences. I concentrate on properties of hadron-nucleus interactions, and I
use mean depth of shower maximum as a function of primary energy to illustrate
my main points. I will contrast these models with models that use a more naive
treatment of hadronic interactions in nuclei but which have been successfully
used to interpret measurements of depth of shower maximum.
