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 ′ bosons as they appear in E 6 and left-right unification models, the sequential 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 constrained (sin θ < 0.01). The lower mass limits are generally of the order of several hundred GeV and competitive with collider bounds. The exception is the Z ψ boson, whose vector couplings vanish and whose limits are weaker. The results change little when the ρ parameter is allowed, which corresponds to a completely arbitrary Higgs sector. On the other hand, in specific models with minimal Higgs structures the limits are generally pushed into the TeV region.The possibility of additional neutral gauge bosons, Z ′ s, is among the best motivated types of physics beyond the Standard Model (SM). They are predicted by most unifying theories, such as Grand Unified Theories (GUTs), left-right unification, superstring theories and their strong coupling generalizations. In many cases their masses remain unpredicted and may or may not be of the electroweak scale. In the context of superstring models, however, which are much more constrained than purely field theoretical models, they are often predicted to arise at the electroweak scale, as we will discuss below. In this paper we consider six different types of Z ′ bosons:1. The Z χ boson is defined by SO(10) → SU(5) × U(1) χ . This boson is also the unique solution to the conditions of (i) family universality, (ii) no extra matter other than the right-handed neutrino, (iii) absence of gauge and mixed gauge/gravitational anomalies, and (iv) orthogonality to the hypercharge generator. In the context of a minimal SO(10) GUT, conditions (i) and (ii) are satisfied by assumption, while (iii) and (iv) are automatic. Relaxing condition (iv) allows other solutions (including the Z LR below) which differ from the Z χ by a shift proportional to the third component of the right-handed isospin generator.2. The Z ψ boson is defined by E 6 → SO(10)×U(1) ψ . It possesses only axial-vector couplings to the ordinary fermions. As a consequence it is the least constrained of our examples.