  This talk presents work concepts and results for the determination of the
fine structure constant $\alpha$ at the $Z_0$ mass resonance. The problem
consisting of the break-down of global duality for singular integral weights is
circumvented by using a polynomial fit which mimics this weight function. This
method is conservative in the sense that it is mostly independent of special
assumptions. In this context the difference between local and global duality is
explained.
