Summary: A general concept of holonomy scattering is defined. It applies, among other things, to imply a nontrivial (generally, inelastic) scattering amplitude for the scattering of pure flux tubes off one another, when these fluxes are non-Abelian and do not commute. The amplitudes for such processes, as well as the original Aharonov-Bohm cross section, are calculated directly from an expression for the propagator with a definite winding number.