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The elliptic flow of inclusive and direct photons was measured at mid-rapidity in two centrality classes 0–20% and 20–40% in Pb–Pb collisions at √sNN=2.76TeV by ALICE. Photons were detected with the highly segmented electromagnetic calorimeter PHOS and via conversions in the detector material with the e+e−pairs reconstructed in the central tracking system. The results of the two methods were combined and the direct-photon elliptic flow was extracted in the transverse momentum range 0.9 <pT<6.2GeV/c. A comparison to RHIC data shows a similar magnitude of the measured direct-photon elliptic flow. Hydrodynamic and transport model calculations are systematically lower than the data, but are found to be compatible.