  We perform a systematic study of the possible loosely bound states composed
of two charmed baryons or a charmed baryon and an anti-charmed baryon within
the framework of the one boson exchange (OBE) model. We consider not only the
$\pi$ exchange but also the $\eta$, $\rho$, $\omega$, $\phi$ and $\sigma$
exchanges. The $S-D$ mixing effects for the spin-triplets are also taken into
account. With the derived effective potentials, we calculate the binding
energies and root-mean-square (RMS) radii for the systems
$\Lambda_c\Lambda_c(\bar{\Lambda}_c)$, $\Xi_c\Xi_c(\bar{\Xi}_c)$,
$\Sigma_c\Sigma_c(\bar{\Sigma}_c)$,
$\Xi_c^\prime\Xi_c^\prime(\bar{\Xi}_c^\prime)$ and
$\Omega_c\Omega_c(\bar{\Omega}_c)$. Our numerical results indicate that: (1)
the H-dibaryon-like state $\Lambda_c\Lambda_c$ does not exist; (2) there may
exist four loosely bound deuteron-like states $\Xi_c\Xi_c$ and
$\Xi_c^\prime\Xi_c^\prime$ with small binding energies and large RMS radii.
