Tests on the Hierarchy of Trilinear and Quadrilinear Weak Bosons Couplings at the NLC and Comparison with the LHC/SSC

I first review a few basic guiding principles that lead to the notion of a hierarchy of couplings in searches of New Physics involving weak bosons processes. The hierarchies within a linear and a non-linear realization of symmetry breaking are compared to the usual {\em phenomenological} parameterization of the $WWV$ vertex. Limits that one expects to obtain at the NLC(500GeV) and LHC/SSC on the tri-linear and quadri-linear anomalous $W$ couplings are compared. The cleanness of an \epm gives the NLC a clear advantage in constraining the tri-linear couplings. However, with only" $500$GeV, the \epm is not competitive with $pp$ colliders in probing the quadri-linear couplings. An interpretation in terms of scalar-like and vector-like models is given and I argue that in the presence of a light (or not-so-heavy") Higgs, the New Physics affecting the $W$ sector would be easier to pin-down with a moderate energy \epm machine.