  We calculate the mixing angles between the spin--1/2,
$\Xi_{bc}$--$\Xi^\prime_{bc}$ and $\Omega_{bc}$--$\Omega^\prime_{bc}$ states of
doubly heavy baryons within the QCD sum rules method. It is found that the
mixing angles are large and have the values $\varphi_{\Xi_{bc}} = 16^0 \pm 5^0$
and $\varphi_{\Omega_{bc}} = 18^0 \pm 6^0$, respectively. The mixing angles are
slightly smaller compared to the predictions of the non--relativistic quark
model, $\varphi_{\Xi_{bc}} = 25.5^0$ and $\varphi_{\Omega_{bc}} = 25.9^0$.
