  This paper is devoted to the study of the process $\epem\to J/\psi X(3940)$
in the framework of light cone formalism. In our calculation two hypotheses
about the structure of X(3940) meson are considered: X(3940) is $3^1$S$_0$
state and X(3940) is one of $2^3$P states. The former hypothesis leads to a
good agreements with the cross section measured at the experiment. As to the
latter one, it is proposed a mechanism that allows one to understand the
suppression of 2P mesons production in hard processes.
