  We use the QCD sum rules for the three point correlation functions to compute
the strong coupling constants of the meson vertices $\eta_c D^* D$ and $\eta_c
D_s^* D_s$. We consider perturbative and non-perturbative contributions,
working up to dimension five on the OPE. The vertices were studied considering
that each one of its three mesons are off-shell alternately. The vertex
coupling constant is evaluated through the extrapolation of the three different
form factors. The results obtained for the coupling constants are $g_{\eta_c
D^* D} = 5.23^{+1.80}_{-1.38}$ and $g_{\eta_c D_s^*
  D_s}=5.55^{+1.29}_{-1.55}$.
