  We study the time evolution of an initially excited many-body state in a
finite system of interacting Fermi-particles in the situation when the
interaction gives rise to the ``chaotic'' structure of compound states. This
situation is generic for highly excited many-particle states in quantum
systems, such as heavy nuclei, complex atoms, quantum dots, spin systems, and
quantum computers. For a strong interaction the leading term for the return
probability $W(t)$ has the form $W(t)\simeq \exp (-\Delta_E^2t^2)$ with
$\Delta_E^2$ as the variance of the strength function. The conventional
exponential linear dependence $W(t)=C\exp (-\Gamma t)$ formally arises for a
very large time. However, the prefactor $C$ turns out to be exponentially
large, thus resulting in a strong difference from the conventional estimate for
$W(t)$.
