  The present paper is devoted to finding a necessary and sufficient condition
on the occurence of scattering for the regularly hyperbolic systems with
time-dependent coefficients whose time-derivatives are integrable over the real
line. More precisely, it will be shown that the solutions are asymptotically
free if the coefficients are stable in the sense of the Riemann integrability
as time goes to infinity, while each nontrivial solution is never
asymptotically free provided that the coefficients are not R-stable as times
goes to infinity. As a by-product, the scattering operator can be constructed.
It is expected that the results obtained in the present paper would be brought
into the study of the asymptotic behaviour of Kirchhoff systems.
