Inclusive jet production (e + e − → e + e − + jet + X) is studied in collisions of quasi-real photons radiated by the LEP beams at e + e − centre-ofmass energies √ s ee from 189 to 209 GeV. Jets are reconstructed using the k ⊥ jet algorithm. The inclusive differential cross-section is measured as a function of the jet transverse momentum, p jet T , in the range 5 < p jet T < 40 GeV for pseudo-rapidities, η jet , in the range −1.5 < η jet < 1.5. The results are compared to predictions of perturbative QCD in next-to-leading order in the strong coupling constant.