Lifetimes of doubly charmed baryons:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>Ξ</mml:mi></mml:mrow><mml:mrow><mml:mi>cc</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>Ξ</mml:mi></mml:mrow><mml:mrow><mml:mi>cc</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mo>+</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>

We perform a detailed investigation of total lifetimes for the ${\ensuremath{\Xi}}_{\mathrm{cc}}^{++}$ and ${\ensuremath{\Xi}}_{\mathrm{cc}}^{+}$ baryons in the framework of operator product expansion over the inverse mass of the charmed quark, whereas, to estimate matrix elements of operators obtained in operator product expansion, some approximations of nonrelativistic QCD are used. This approach allows one to take into account the corrections to the spectator decays of c quarks, which reflect the fact that these quarks are bound as well as the contributions connected to the effects of both the Pauli interference for the ${\ensuremath{\Xi}}_{\mathrm{cc}}^{++}$ baryon and the weak scattering for the ${\ensuremath{\Xi}}_{\mathrm{cc}}^{+}$ baryon. The realization of such a program leads to the following estimates for the total lifetimes of doubly charmed baryons: ${\ensuremath{\tau}}_{{\ensuremath{\Xi}}_{\mathrm{cc}}^{++}}=0.43\ifmmode\pm\else\textpm\fi{}0.11 \mathrm{ps}$ and ${\ensuremath{\tau}}_{{\ensuremath{\Xi}}_{\mathrm{cc}}^{+}}=0.11\ifmmode\pm\else\textpm\fi{}0.03 \mathrm{ps}.$

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