We discuss $\gamma^* \gamma^* \to \eta_c(1S)\, , \,\eta_c(2S)$ transition form factors

for both virtual photons. The general formula is given. We use different models for the

$c \bar c$ wave function obtained from the solution of the Schr\"odinger equation for

different $c \bar c$ potentials: harmonic oscillator, Cornell, logarithmic, power-law, Coulomb

and Buchm\"uller-Tye. We showed some examples of wave functions in the Light Front

representation as well as in the rest frame of $c \bar c$ pair. We compare our results to

the BaBar experimental data for $\eta_c(1S)$, for one real and one virtual photon,

and to the values collected by the Particle Data Group for $F(0,0)$, decay width

$\Gamma_{\gamma \gamma}$ and decay constant $f_{\eta_c}$.

We also considered the non-relativistic limit for $F(0,0)$ form factor with

the wave function at the origin $R(0)$.