The value of the QED running coupling constant alpha(m(z)(2)) is very
important for precision tests of the standard model. A purely theoreti
cal calculation of the hadronic part Delta alpha(h)(m(z)(2)) using QCD
and the analytic properties of the vacuum polarisation tensor is pres
ented. We obtain Delta alpha(h)(m(z)(2))=0.0267+/-0.0011.