[en] We present measurements of the hadronic photon structure function F₂^γ(x), in two Q² ranges with mean values of 5.9 GeV² and 14.7 GeV². The data were taken by the OPAL experiment at LEP, with √s close to the Z⁰ mass and correspond to an integrated e⁺e^- luminosity of 44.8 pb^-1. In the context of a QCD-based model we find the quark transverse momentum cutoff separating the vector meson dominance (VMD) and perturbative QCD regions to be 0.27 ± 0.10 GeV. We confirm that there is a significant pointlike component of the photon when the probe photon has Q² > 4 GeV². Our measurements extend to lower values of x than any previous experiment, and no increase of F₂^γ(x) is observed. (orig.)