  In this paper the processes $e^+ e^- \to J/\Psi J/\Psi, J/\Psi \psi', \psi'
\psi'$ are considered in the framework of light cone formalism. An important
distinction of this approach in comparison to the approaches used in other
papers is that relativistic and leading logarithmic radiative corrections to
the cross section can be easily resummed within light cone formalism. In this
paper the effect of this resummation is studied. It is shown that this effect
is important especially for the production of higher charmonium mesons. The
predicted cross sections are in agreement with the upper bounds set by Belle
collaboration.
