  We consider phenomenological constraints on the mass $M_{Z^{\prime}}$ and the
two mixing angles $\theta_R$ and $\xi$ of the neutral sector in a very general
class of $SU(2)_L \times SU(2)_R \times U(1)$ models using electroweak data. We
do not make any specific assumptions such as left-right symmetry or the Higgs
structure. The analysis of the neutral sector has the advantage that it has
relatively fewer parameters compared to the charged sector since the
Cabibbo-Kobayashi-Maskawa (CKM) matrix elements in the right-handed sector do
not enter into the analysis, hence the number of various possibilities from a
big parameter space is reduced. We utilize theoretical considerations on the
masses of the gauge particles and the mixing angles. We combine the precision
electroweak data from LEP I and the low-energy neutral-current experimental
data to constrain the parameters introduced in the model. It turns out that
$M_{Z^{\prime}}> 400$ GeV, $-0.0028 <\xi <0.0065$ with little constraint on
$\theta_R$. In the left-right symmetric theory, $M_{Z^{\prime}}$ should be
larger than 900 GeV. With these constraints, we compare the values for $\sigma
(e^+ e^- \to \mu^+ \mu^-)$, $\sigma (e^+ e^- \to b\bar{b})$ and $A_{FB}^{\ell}$
at LEP II with experimental values.
