The search for an additional heavy gauge boson Z' is described. The mo
dels 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 deter
mine limits on the Z-Z' gauge boson mixing angle and on the Z' mass. F
or Z' masses above the direct limits, we obtain the following allowed
ranges of the mixing angle, theta(M), at the 95% confidence level: -0.
004 less-than-or-equal-to theta(M) less-than-or-equal-to 0.015 for the
chi model, -0.003 less-than-or-equal-to theta(M) less-than-or-equal-t
o 0.020 for the psi model, -0.029 less-than-or-equal-to theta(M) less-
than-or-equal-to 0.010 for the eta model, -0.002 less-than-or-equal-to
theta(M) less-than-or-equal-to 0.015 for the LR model.