  We have systematically studied the strong and radiative decays of the
low-lying $1P$-wave doubly charmed baryons. Some interesting observations are:
(i) The states $\Xi_{cc}^*$ and $\Omega_{cc}^*$ with $J^P=3/2^+$ have a fairly
large decay rate into the $\Xi_{cc}\gamma$ and $\Omega_{cc}\gamma$ channels
with a width $\sim 15$ and $\sim7$ keV, respectively. (ii) The lowest lying
excited doubly charmed baryons are dominated by the $1P$ $\rho$ mode
excitations, which should be quite narrow states. They decay into the ground
state with $J^P=1/2^+$ through the radiative transitions with a significant
ratio. (iii) The total decay widths of the first orbital excitations of
$\lambda$ mode ($1P_{\lambda}$ states with $J^P=1/2^-$, $3/2^-$, $5/2^-$) are
about $\Gamma\sim100$ MeV, and the ratio between the radiative and hadronic
decay widths is about $\mathcal{O}(10^{-3})$.
