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We derive expressions for the differential distributions and the total crosssection of double- parton interaction in direct photon interaction with protonand nuclei. We demonstrate that in this case the cross section is more directlyrelated to the nucleon generalized parton distribution than in the case ofdouble parton interactions in the proton - proton collisions. We focus on theproduction of two dijets each containing charm (anticharm) quarks and carrying$x_1,x_2>0.2$ fractions of the photon momentum. Numerical results are presentedfor the case of $\gamma p$ collisions at LHeC, HERA and in the ultraperipheral$AA$ and $pA$ collisions at the LHC. We find that the events of this kind wouldbe abundantly produced at the LHeC. For $\sqrt{s}=1.3$ TeV the expected rate is$2\cdot 10^8$ events for the luminosity $10^{34}$ cm$^{-2}s^{-1}$, the runningtime of $10^6$ s and the transverse cutoff of $p_t>5$ GeV. This would make itfeasible to use these processes for the model independent determination of twoparton GPDs in nucleon and in nuclei. For HERA the total accumulated number ofthe events is also high, but efficiency of the detection of charm seems too lowto study the process. We also find that a significant number of such doubleparton interactions should be produced in $p - Pb$ and $Pb- Pb$ collisions atthe LHC: $\sim 6\cdot 10^4$ for $Pb-Pb$, and $\sim 7 \cdot 10^3$ for $p-Pb$collisions for the same transverse momentum cutoff.

Double parton interactions in $\gamma p, \gamma A$ collisions in the direct photon kinematics