  We derive a method for a common treatment of Z' exchange, QED corrections,
and weak loops. It is based on the form factor approach to the description of
weak loop corrections to partial Z widths and cross sections. Problems
connected with ZZ' mixing are discussed with special care. Our theoretical
results are applied to the package ZFITTER. We demonstrate two different ways
to the data analysis - one based on an extension of the standard model cross
sections, the other on model-independent formulae together with the Z width
calculations in presence of a Z'. With the resulting package ZEFIT+ZFITTER,
LEP1 data from fermion pair production, including Bhabha scattering, can be
analysed on, but also off the Z peak. Further, the code may be used at very
high energies, e.g. in the region of a possible future linear e+e- collider.
