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The azimuthal anisotropy coefficient v2 of prompt D0, D+, D∗+ and D+s mesons was measured in mid-central (30-50% centrality class) Pb-Pb collisions at a centre-of-mass energy per nucleon pair sNN−−−√=5.02 TeV, with the ALICE detector at the LHC. The D mesons were reconstructed via their hadronic decays at mid-rapidity, |y|<0.8, in the transverse momentum interval 1<pT<24 GeV/c. The measured D-meson v2 has similar values as that of charged pions. The D+s v2, measured for the first time, is found to be compatible with that of non-strange D mesons. The measurements are compared with theoretical calculations of charm-quark transport in a hydrodynamically expanding medium and have the potential to constrain medium parameters.