  The lifetimes of doubly charmed hadrons are analyzed within the framework of
the heavy quark expansion (HQE). Lifetime differences arise from spectator
effects such as $W$-exchange and Pauli interference. The $\Xi_{cc}^{++}$ baryon
is longest-lived in the doubly charmed baryon system owing to the destructive
Pauli interference absent in the $\Xi_{cc}^+$ and $\Omega_{cc}^+$. In the
presence of dimension-7 contributions, its lifetime is reduced from
$\sim5.2\times 10^{-13}s$ to $\sim3.0\times 10^{-13}s$. The $\Xi_{cc}^{+}$
baryon has the shortest lifetime of order $0.45\times 10^{-13}s$ due to a large
contribution from the $W$-exchange box diagram. It is difficult to make a
precise quantitative statement on the lifetime of $\Omega_{cc}^+$. Contrary to
$\Xi_{cc}$ baryons, $\tau(\Omega_{cc}^+)$ becomes longer in the presence of
dimension-7 effects and the Pauli interference $\Gamma^{\rm int}_+$ even
becomes negative. This implies that the subleading corrections are too large to
justify the validity of the HQE. Demanding the rate $\Gamma^{\rm int}_+$ to be
positive for a sensible HQE, we conjecture that the $\Omega_c^0$ lifetime lies
in the range of $(0.75\sim 1.80)\times 10^{-13}s$. The lifetime hierarchy
pattern is $\tau(\Xi_{cc}^{++})>\tau(\Omega_{cc}^+)>\tau(\Xi_{cc}^+)$ and the
lifetime ratio $\tau(\Xi_{cc}^{++})/\tau(\Xi_{cc}^+)$ is predicted to be of
order 6.7.
