© 2017, CERN for the benefit of the ALICE collaboration. The transverse momentum (pT) spectra and elliptic flow coefficient (v2) of deuterons and anti-deuterons at mid-rapidity (| y| < 0.5) are measured with the ALICE detector at the LHC in Pb–Pb collisions at sNN = 2.76 TeV. The measurement of the pTspectra of (anti-)deuterons is done up to 8 GeV/ c in 0–10% centrality class and up to 6 GeV/ c in 10–20% and 20–40% centrality classes. The v2is measured in the 0.8 < pT<5 GeV/ c interval and in six different centrality intervals (0–5, 5–10, 10–20, 20–30, 30–40 and 40–50%) using the scalar product technique. Measured π±, K±and p+p ¯ transverse-momentum spectra and v2are used to predict the deuteron pTspectra and v2within the Blast-Wave model. The predictions are able to reproduce the v2coefficient in the measured pTrange and the transverse-momentum spectra for pT> 1.8 GeV/ c within the experimental uncertainties. The measurement of the coalescence parameter B2is performed, showing a pTdependence in contrast with the simplest coalescence model, which fails to reproduce also the measured v2coefficient. In addition, the coalescence parameter B2and the elliptic flow coefficient in the 20–40% centrality interval are compared with the AMPT model which is able, in its version without string melting, to reproduce the measured v2(pT) and the B2(pT) trend.