Title: Measurement of the Running of the Fine Structure Constant Small-angle Bhabha scattering data recorded at the Z resonance and large angle Bhabha scattering data recorded at sqrt(s)=189 GeV by the L3 detector at LEP are used to measure the running of the effictive fine-structure constant for spacelike momentum transfers. The results are in agreement with theoretical predicions. Parallel session #PA 5 Plenary session #Pl 6a **************************************************** * paper 197 CERN-EP 2000/005, Phys.Lett.B accepted * ****************************************************