  The next-to-leading nonperturbative contributions to heavy quarkonium systems
are calculated. The applicability of the Voloshin-Leutwyler approach to heavy
quarkonia systems for the physical cases of Bottomonium and Charmonium is
investigated. We study whether the background gluon field correlation time can
be considered to be infinity or not, by calculating the leading correction to
this assumption and checking whether the expansion is under control. A
phenomenological analysis of our results is also performed. The results make us
feel optimistic about the $\Upsilon(1S)$ and to a lesser extent about the
$J/\psi$ but do not about higher levels. We also briefly discuss the connection
with different models where a finite gluon correlation time is introduced.
