  In this article, we study the mass spectra of baryons containing two heavy
quarks; charm-charm ($cc$) and bottom-charm ($bc$) with a light quark ($u,d,s$)
within the framework of Regge phenomenology. With the assumption of linear
Regge trajectories we have derived the relations between slope ratios,
intercepts, and baryon masses. Using these relations, the ground state masses
of $\Xi_{cc}$, $\Xi_{bc}$, $\Omega_{cc}$, and $\Omega_{bc}$ baryons are
obtained. The values of Regge slopes and Regge intercepts are extracted for
these baryons to estimate the excited state masses in both the ($J,M^{2}$) and
($n,M^{2}$) planes. Our obtained results are compared with the experimental
observations where available and other theoretical predictions, which could be
a valuable addition to the interpretations of experimentally unknown heavy
baryon spectra.
