[en] The value of the strong coupling constant α_s is determined from a combined analysis of the global event shape variables thrust, heavy jet mass and total and wide jet broadening. The extraction of α_s includes the full calculation of O(α_s²) terms and leading and next-to-leading logarithms resummed to all orders of α_s. The analysis is based on data taken with the DELPHI detector at LEP during 1991 and 1992. The dependence of the result on the detailed matching of the resummed and fixed order terms is studied. The result from the combined theory is compared with values coming from a pure NLLA analysis and as pure O(α_s²) analysis, respectively. It is found that the inclusion of the resummed logarithms allows the description of the data in the two jet range and reduces the scale dependence of α_s(M_Z²) compared to pure O(α_s²) theory. The value using the combined NLLA+O(α_s²) theory at the scale μ²=M_Z² is α_S(M_Z²)=0.118±0.007. The running of α_s is measured from the 1991 data in an energy range from 88.5 to 93.7 GeV. The slope of α_s obtained at the Z peak is dα_s/dQ/_Q=Mz=-(2.9±2.8)x10^-4GeV^-1. This value is compatible with QCD and exludes an abelian gluon model with more than two standard deviations. (orig.)