Electroweak precision data are analysed in extensions of the Standard
Model with modifications of the vector boson propagators and the Zbb c
ouplings. Assuming general vector and axial vector couplings between b
quarks and the Z boson, we derive the specific Zbb vertex contributio
ns in terms of the partial widths Gamma(<b(b)over bar>) - Gamma(<d(d)o
ver bar>) from the data. Within special classes of models (models with
modifications exclusively of the vector boson propagators, the genera
l 2-Higgs doublet model, and the minimal supersymmetric standard model
in the limit of heavy susy particles) constraints on the models are d
erived and discussed. In particular we determine upper bounds on the t
op quark mass in the considered classes of generalized electroweak mod
els. We find that due to the restrictions of the Zbb vertex the top qu
ark mass cannot be higher than in the minimal model.