  We analyse the possible existence of non-perturbative contributions in heavy
$\bar Q Q$ systems ($\bar Q$ and $Q$ need not have the same flavour) which
cannot be expressed in terms of local condensates. Starting from QCD, with well
defined approximations and splitting properly the fields into large and small
momentum components, we derive an effective lagrangian where hard gluons (in
the non-relativistic aproximation) have been integrated out. The large momentum
contributions (which are dominant) are calculated using Coulomb type states.
Besides the usual condensate corrections, we see the possibility of new
non-perturbative contributions. We parametrize them in terms of two low
momentum correlators with Coulomb bound state energy insertions $E_n$. We
realize that the Heavy Quark Effective lagrangian can be used in these
correlators.
  We calculate the corrections that they give rise to in the decay constant,
the bound state energy and the matrix elements of bilinear currents at zero
recoil. We study the cut-off dependence of the new contributions and we see
that it matches perfectly with that of the large momentum contributions.
  We consider two situations in detail: i) $E_n>> \Lambda_{QCD}$ ($M_Q
\rightarrow \infty$) and ii) $E_n << \Lambda_{QCD}$, and briefly discuss the
expected size of the new contributions in $\Upsilon$ , $J/\Psi$ and
$B_{c}^{\ast}$ systems.
