The measurement of the invisible Z-boson decay width at e(+)e(-) colliders can be done "indirectly," by subtracting the Z-boson visible partial widths from the Z-boson total width, or "directly," from the process e(+)e(-)-->gammanu(nu) over bar. Both procedures are sensitive to different types of new physics and provide information about the couplings of the neutrinos to the Z boson. At present, measurements at CERN LEP and CHARM II are capable of constraining the left-handed Znu(nu) over bar coupling, 0.45less than or similar tog(L)less than or similar to0.5, while the right-handed one is only mildly bounded, \g(R)\less than or equal to0.2. We show that measurements at a future e(+)e(-) linear collider at different center-of-mass energies, roots=m(Z) and rootsapproximate to170 GeV, would translate into a markedly more precise measurement of the Znu(nu) over bar couplings. A statistically significant deviation from standard model predictions will point toward different new physics mechanisms, depending on whether the discrepancy appears in the direct or the indirect measurement of the invisible Z width. We discuss some scenarios which illustrate the ability of different invisible Z-boson decay measurements to constrain new physics beyond the standard model.