to explore the nonspectator effects, where their importance is increased. Here we would like to note, that in the case of systems with two heavy quarks, the hypothesis on the quark-hadron duality is more justified, and, so, the results of OPE-based approach turn out to be more reliable. For these baryons we can apply a method, based on the combined HQET-NRQCD techniques [@HQET; @NRQCD; @Beneke], if we use the quark-diquark picture for the bound states. The expansion in the inverse heavy quark mass for the heavy diquark $QQ^\prime$ is a straightforward generalization of these techniques in the mesonic decays of $B_c$ [@NRQCD; @Beneke], with the difference that, instead of the color-singlet systems, we deal with the color–anti-triplet ones, with the appropriate account for the interaction with the light quark. First estimates of the lifetimes for the doubly heavy baryons $\Xi_{cc}^{\diamond}$ and $\Xi_{bc}^{\diamond}$ were recently performed in [@DHD1; @DHD2]. Using the same approach, but different values of parameters[^3] a repetition of our results for the case of doubly charmed baryons was done in [@Guberina]. The spectroscopic characteristics of baryons with two heavy quarks and the mechanisms of their production in different interactions were discussed in refs. [@DHS1; @DHS2; @DHS3; @DHSR] and 