The effect of new operators that only modify the bosonic couplings of the
Higgs boson, without altering the WW\gamma or WWZ three-point functions, are
examined in the e+e- -> ZZ\gamma and Z\gamma\gamma processes. We analyse the
constraints on these interactions that can be imposed by the LEP II collider at
CERN and at the Next Linear Collider.Comment: 7 pages, RevTeX, 3 postscript figure