  We present examples demonstrating that quasi-equilibrium
fluctuation-dissipation behavior at short time differences is not a generic
feature of systems with slow non-equilibrium dynamics. We analyze in detail the
non-equilibrium fluctuation-dissipation ratio X(t,tw) associated with a
defect-pair observable in the Glauber-Ising spin chain. It turns out that $X
\neq 1$ throughout the short-time regime and in particular X(tw,tw) = 3/4 for
$tw \to \infty$. The analysis is extended to observables detecting defects at a
finite distance from each other, where similar violations of quasi-equilibrium
behaviour are found. We discuss our results in the context of metastable
states, which suggests that a violation of short-time quasi-equilibrium
behavior could occur in general glassy systems for appropriately chosen
observables.

Statistical Mechanics