Recently, calculations which consider the implications of anomalous trilinear
gauge-boson couplings, both at tree-level and in loop-induced processes, have
been criticized on the grounds that the lagrangians employed are not \gwk gauge
invariant. We prove that, in fact, the general Lorentz-invariant and $U(1)_\em$
invariant but {\it not} $SU_L(2)\times U_Y(1)$ invariant action is equivalent
to the general lagrangian in which $SU_L(2)\times U_Y(1)$ appears but is
nonlinearly realized. We demonstrate this equivalence in an explicit
calculation, and show how it is reconciled with loop calculations in which the
different formulations can (superficially) appear to give different answers. In
this sense any effective theory containing light spin-one particles is seen to
be automatically gauge invariant.
