  We discuss how to describe time-dependent phenomena in string theory like the
decay of unstable D-branes with the help of the world-sheet formulation. It is
shown in a nontrivial well-controlled example that the coupling of the tachyons
to propagating on-shell modes which escape to infinity can lead to
time-dependent relaxation into a stationary final state. The final state
corresponds to a fixed point of the RG flow generated by the relevant field
from which the tachyon vertex operator is constructed. On the way we set up a
fairly general formalism for the description of slow time-dependent phenomena
with the help of conformal perturbation theory on the world-sheet.
