  We obtain the partial-wave unitarity constraints on the lowest-dimension
effective operators which generate anomalous quartic gauge couplings but leave
the triple gauge couplings unaffected. We consider operator expansions with
linear and nonlinear realizations of the electroweak symmetry and explore the
multidimensional parameter space of the coefficients of the relevant operators:
20 dimension-eight operators in the linear expansion and 5 ${\cal O}(p^4)$
operators in the derivative expansion. We study two-to-two scattering of
electroweak gauge bosons and Higgs bosons taking into account all coupled
channels and all possible helicity amplitudes for the $J=0,1$ partial waves. In
general, the bounds degrade by factors of a few when several operator
coefficients are considered non-vanishing simultaneously. However, this
requires to consider constraints from both $J=0$ and $J=1$ partial waves for
some sets of operators.
