  In this paper, we discuss the possibility to probe a nearly-degenerate
$Z^{\prime}$-$Z$ system by analyzing the $Z$-lineshape at an electron-positron
collider. Compared with the usual $Z^{\prime}$ in the literature well separated
with the standard model (SM) $Z$ boson in mass, the nearly-degenerate
$Z^{\prime}$-$Z$ mixing affects the observed effective ``oblique parameters''
$\tilde{S}$, $\tilde{T}$, $\tilde{U}$, and the effective deviation of ``number
of neutrino species'' $\delta \tilde{N}_{\nu}$ in a more complicated way and
cannot be simply computed perturbatively up to a particular order. Aiming at
solving this problem, we write down a general simplified effective Lagrangian
and enumerate some parameter spaces corresponding to some typical models, and
suggest a method to extract the constraints by looking into the line-shape of
the $Z$-like resonance at an electron-positron collider.
