  The existence of doubly heavy flavor baryons has not been well established
experimentally so far. In this Letter we systematically investigate the weak
decays of the doubly charmed baryons, $\Xi_{cc}^{++}$ and $\Xi_{cc}^{+}$, which
would be helpful for experimental searches for these particles. The branching
fractions are studied under the factorization hypothesis for the short-distance
contributions and considering the rescattering effect for the long-distance
contributions which are significantly enhanced. Comparing all the decay modes,
we recommend the processes of $\Xi_{cc}^{++}\to \Lambda_c^+K^-\pi^+\pi^+$ and
$\Xi_c^+\pi^+$ as the first priority for experiments to search for the doubly
heavy baryons.
