Infrared and collinear safe event shape distributions and their mean values
are determined using the data taken at five different centre of mass energ
ies above M-Z with the DELPHI detector at LEP. From the event shapes, the s
trong coupling alpha(s) is extracted in O(alpha(s)(2)), NLLA and a combined
scheme using hadronisation corrections evaluated with fragmentation model
generators as well as using an analytical power ansatz. Comparing these mea
surements to those obtained at M-Z, the energy dependence (running) of alph
a(s) is accessible. The logarithmic energy slope of the inverse strong coup
ling is measured to be
d alpha(s)(-1)/d log(E-cm) = 1.39 +/- 0.34 (stat) +/- 0.17(syst),
in good agreement with the QCD expectation of 1.27. (C) 1999 Published by E
lsevier Science B.V. All rights reserved.