  In this work, we perform a systematic study of possible molecular states
composed of two charmed baryons including hidden-charm systems
$\Lambda_c\bar{\Lambda}_c$, $\Sigma_c^{(*)}\bar{\Sigma}_c^{(*)}$, and
$\Lambda_c\bar{\Sigma}_c^{(*)}$, and corresponding double-charm systems
$\Lambda_c\Lambda_c$, $\Sigma_c^{(*)}\Sigma_c^{(*)}$, and
$\Lambda_c\Sigma_c^{(*)}$. With the help of the heavy quark chiral effective
Lagrangians, the interactions are described with $\pi$, $\rho$, $\eta$,
$\omega$, $\phi$, and $\sigma$ exchanges. The potential kernels are
constructed, and inserted into the quasipotential Bethe-Salpeter equation. The
bound states from the interactions considered is studied by searching for the
poles of the scattering amplitude. The results suggest that strong attractions
exist in both hidden-charm and double-charm systems considered in the current
work, and bound states can be produced in most of the systems. More experiment
studies about these molecular states are suggested though the nucleon-nucleon
collison at LHC and nucleon-antinucleon collison at $\rm \bar{P}ANDA$.
