  I discuss double-diffractive (double-elastic) production of the $\eta'$ and
$\eta_c$ mesons in the $pp \to p X p$ reaction within the formalism of
unintegrated gluon distribution functions (UGDF). The contribution of $\gamma^*
\gamma^* \to \eta'$ fusion is estimated. The distributions in the Feynman $x_F$
(or rapidity), transferred four-momenta squared between initial and final
protons ($t_1$, $t_2$) and azimuthal angle difference between outgoing protons
($\Phi$) are calculated and discussed. The results are compared with the WA102
data. Predictions at higher energies are presented.
