A combination of measurements of the inclusive top-quark pair production cross-section performed by ATLAS and CMS in proton–proton collisions at centre-of-mass energies of 7 and 8 TeV at the LHC is presented. The cross-sections are obtained using top-quark pair decays with an opposite-charge electron–muon pair in the final state and with data corresponding to an integrated luminosity of about 5 fb−1 at s$$ \sqrt{s} $$ = 7 TeV and about 20 fb−1 at s$$ \sqrt{s} $$ = 8 TeV for each experiment. The combined cross-sections are determined to be 178.5 ± 4.7 pb at s$$ \sqrt{s} $$ = 7 TeV and 243.3−5.9+6.0$$ {243.3}_{-5.9}^{+6.0} $$ pb at s$$ \sqrt{s} $$ = 8 TeV with a correlation of 0.41, using a reference top-quark mass value of 172.5 GeV. The ratio of the combined cross-sections is determined to be R8/7 = 1.363 ± 0.032. The combined measured cross-sections and their ratio agree well with theory calculations using several parton distribution function (PDF) sets. The values of the top-quark...