We discuss diphoton semi(exclusive) production in ultraperipheral P bP b collisions at energy of √ sNN = 5.5 TeV (LHC). The nuclear calculations are based on equivalent photon approximation in the impact parameter space. The cross sections for elementary γγ → γγ subprocess are calculated including three different mechanisms: box diagrams with leptons and quarks in the loops, a VDM-Regge contribution with virtual intermediate hadronic excitations of the photons and the two-gluon exchange contribution (formally three-loops) to elastic photon-photon scattering in the high-energy approximation. We got relatively high cross sections in P bP b collisions (306 nb). This opens a possibility to study the γγ → γγ (quasi)elastic scattering at the LHC. We find that the cross section for elastic γγ scattering could be measured in the lead-lead collisions for the diphoton invariant mass up to Wγγ ≈ 15 − 20 GeV. We identify region(s) of phase space where the twogluon exchange contribution becomes important ingredient compared to box and nonperturbative VDM-Regge mechanisms. We perform a similar analysis for the pp → ppγγ reaction at energy of √ sNN = 7 and 100 TeV.