We tested several models in which the Standard Model (SM) gauge group is extended by an additional U(1) gauge symmetry against available electroweak precision data to impose limits on the mass of the neutral Z′ boson, MZ′, predicted in all such models, and on the Z−Z′ mixing angle, θZZ′, at 95% C.L. We found lower limits on MZ′ of order 1 TeV in most cases, while θZZ′ was found to be constrained to very small values.