  A search for the production of the $\eta'_c$ meson, the first radial
excitation of the ground state of charmonium $\eta_c$(2980), in the
photon-photon fusion reaction at LEP has been performed using the data
collected by the DELPHI detector during 1992-1996. No evidence of $\eta'_c$
production is found in the mass region 3520--3800 MeV/c^2. An upper limit for
the ratio of the two-photon widths of the $\eta'_c$ and $\eta_c$ is obtained.
