The search for an additional heavy gauge boson Z ~ is described. The models considered are based on either a superstring-motivated E6 or on a left-right symmetry and assume a minimal Higgs sector. Cross sections and asymmetries measured with the L3 detector in the vicinity of the Z resonance during the 1990 and 1991 running periods are used to determine limits on the Z-Z' gauge boson mixing angle and on the Z' mass. For Z' masses above the direct limits, we obtain the following allowed ranges of the mixing angle, 0M, at the 95% confidence level:
- 0.004 ≲ 0M ≲ 0.015 for the X model,
- 0.003 ≲ 0M ≲ 0.020 for the g model,
- 0.029 ≲ 0M ≲ 0.010 for the t/ model,
- 0.002 ≲ 0M ≲ 0.015 for the LR model.