  We investigate the occurrence of exponential relaxation in a certain class of
closed, finite systems on the basis of a time-convolutionless (TCL) projection
operator expansion for a specific class of initial states with vanishing
inhomogeneity. It turns out that exponential behavior is to be expected only if
the leading order predicts the standard separation of timescales and if,
furthermore, all higher orders remain negligible for the full relaxation time.
The latter, however, is shown to depend not only on the perturbation
(interaction) strength, but also crucially on the structure of the perturbation
matrix. It is shown that perturbations yielding exponential relaxation have to
fulfill certain criteria, one of which relates to the so-called ``Van Hove
structure''. All our results are verified by the numerical integration of the
full time-dependent Schroedinger equation.
