  We study the process of relaxation back to thermal equilibrium in
$(1+1)$-dimensional conformal field theory at finite temperature. When the size
of the system is much larger than the inverse temperature, perturbations decay
exponentially with time. On the other hand, when the inverse temperature is
large, the relaxation is oscillatory with characteristic period set by the size
of the system. We then analyse the intermediate regime in two specific models,
namely free fermions, and a strongly coupled large $\tt k$ conformal field
theory which is dual to string theory on $(2+1)$-dimensional anti-de Sitter
spacetime. In the latter case, there is a sharp transition between the two
regimes in the ${\tt k}=\infty$ limit, which is a manifestation of the
gravitational Hawking-Page phase transition. In particular, we establish a
direct connection between quasinormal and normal modes of the gravity system,
and the decaying and oscillating behaviour of the conformal field theory.
