In the leading order of perturbative QCD we calculate the total and differential cross sections for the hadronic production of doubly charmed baryons ${\Xi }_{\mathrm{cc}}$ and ${\Xi }_{\mathrm{cc}}^{*}$ in different experiments. The experimental evaluation of the cross sections for the $J/\psi +D+\overline{D}$ production would allow us to decrease the uncertainty in the determination of cross sections for the doubly charmed baryons due to the choice of ${\alpha }_s$ and $m_c.$ We show that in the HERA-B and E781 experiments with fixed tagets the suppression of the ${\Xi }_{\mathrm{cc}}$ and ${\Xi }_{\mathrm{cc}}^{*}$ production to the yield of $c\overline{c}$ pairs is a value of the order of ${10}^{-6}-{10}^{-5}$, whereas at the Fermilab Tevatron and CERN LHC colliders it is about ${10}^{-4}-{10}^{-3}$. In the E781 experiment the observation of ${\Xi }_{\mathrm{cc}}$ and ${\Xi }_{\mathrm{cc}}^{*}$ is practically impossible. At the HERA-B and Tevatron facilities one can expect ${10}^5$ events with the double charm, and at LHC one has about ${10}^9$ events.

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