An analysis of global event-shape variables has been carried out for the reaction e+e−→Z0→hadrons to measure the strong coupling constant αs. This study is based on 52 720 hadronic events obtained in 1989/90 with the ALEPH detector at the LEP collider at energies near the peak of the Z-resonance. In order to determine αs, second order QCD predictions modified by effects of perturbative higher orders and hadronization were fitted to the experimental distributions of event-shape variables. From a detailed analysis of the theoretical uncertainties we find that this approach is best justified for the differential two-jet rate, from which we obtain αs(MZ2) = 0.121 ± 0.002(stat.)±0.003(sys.)±0.007(theor.) using a renormalization scale . The dependence of αs(MZ2) on ω is parameterized. For scales mb<ω<MZ the result varies by −0.012+0.007.