  We construct an effective Lagrangian for low energy hadronic interactions
through an infinite expansion in inverse powers of the low energy cutoff
$\Lambda_\chi$ of all possible chiral invariant non-renormalizable interactions
between quarks and mesons degrees of freedom. We restrict our analysis to the
leading terms in the $1/N_c$ expansion. The effective expansion is in
$(\mu^2/\cutoff^2 )^P \ln (\cutoff^2/\mu^2 )^Q$. Concerning the next-to-leading
order, we show that, while the pure $\mu^2/\cutoff^2 $ corrections cannot be
traced back to a finite number of non renormalizable interactions, those of
order $(\mu^2/\cutoff^2 ) \ln (\cutoff^2/\mu^2 )$ receive contributions from a
finite set of $1/\cutoff^2$ terms. Their presence modifies the behaviour of
observable quantities in the intermediate $Q^2$ region. We explicitely discuss
their relevance for the two point vector currents Green's function.
