Limits on the quartic couplings Zγγγ and ZZγγ from e+e- colliders

We obtain limits on the quartic neutral gauge bosons couplings Z gamma gamma gamma and ZZ gamma gamma using LEP 2 data published by the L3 Collaboration on the reactions e(+)e(-) -> gamma gamma gamma, Z gamma gamma. We also obtain 95% C.L. limits on these couplings at the future linear colliders' energies. The LEP 2 data induce limits of order 10(-5) GeV-4 for the Z gamma gamma gamma couplings and of order 10(-3) GeV-2 for the ZZ gamma gamma couplings, which are still above the respective standard model predictions. Future e(+)e(-) linear colliders may improve these limits by one or two orders of magnitude.