We present a determination of the strong coupling constant from a fit of QCD predictions for six event-shape variables, calculated at next-to-next-to-leading order (NNLO) and matched to resummation in the next-to-leading-logarithmic approximation (NLLA). These event shapes have been measured in e+e− annihilations at LEP, where the data we use have been collected by the ALEPH detector at centre-of-mass energies between 91 and 206 GeV. Compared to purely fixed order NNLO fits, we observe that the central fit values are hardly affected, but the systematic uncertainty is larger because the NLLA part re-introduces relatively large uncertainties from scale variations. By combining the results for six event-shape variables and eight centre-of-mass energies, we find αs(MZ) = 0.1224 ± 0.0009 (stat) ± 0.0009 (exp) ± 0.0012 (had) ± 0.0035 (theo), which improves previously published measurements at NLO+NLLA. We also carry out a detailed investigation of hadronisation corrections, using a large set of Monte Carlo generator predictions.