Indirect precision data are used to constrain the masses of possible extra
Z' bosons and their mixings with the ordinary Z. We study a variety of Z' b
osons as they appear in E-sigma, and left-right unification models, the seq
uential Z boson, and the example of an additional U(1) in a concrete model
from heterotic string theory. In all cases the mixings are severely constra
ined (sin theta < 0.01). The lower mass limits are generally of the order o
f several hundred GeV and competitive with collider bounds. The exception i
s the Z(psi) boson, whose vector couplings vanish and whose limits are: wea
ker. The results change little when the rho parameter is allowed, which cor
responds to a completely arbitrary Higgs sector. On the other hand, in spec
ific models with minimal Higgs structures the limits are generally pushed i
nto the TeV region. (C) 1999 Elsevier Science B.V. All rights reserved.