The full microscopic structure of macroscopic shocks is obtained exact
ly in the one-dimensional totally asymmetric simple exclusion process
from the complete solution of the uniform stationary non-equilibrium s
tate of a system containing two types of particles-<<first>> and <<sec
ond>> class. The width of the shock as seen from a second-class partic
le diverges as the inverse square of its strength when the latter goes
to zero. In that limit the steady state exhibits long-range correlati
ons and weakly bound states of second-class particles.