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We consider the transverse-momentum (pT) distribution of Zγ pairs produced in hadronic collisions. Logarithmically enhanced contributions at small pT are resummed to all orders in QCD perturbation theory and combined with the fixed-order prediction. We achieve the most advanced prediction for the Zγ pT spectrum by matching next-to-next-to-next-to-leading logarithmic (N3LL) resummation to the integrated cross section at next-to-next-to-leading order (NNLO). By considering ℓ+ℓ−γ production at the fully differential level, including spin correlations, interferences and off-shell effects, arbitrary cuts can be applied to the leptons and the photon. We present results at the LHC in presence of fiducial cuts and find agreement with the 13TeV ATLAS data at the few-percent level.