  We examine the Lorentz non-invariance ambiguity in longitudinal weak-boson
scatterings and the precise conditions for the validity of the Equivalence
Theorem (ET). {\it Safe} Lorentz frames for applying the ET are defined, and
the intrinsic connection between the longitudinal weak-boson scatterings and
probing the symmetry breaking sector is analyzed. A universal precise
formulation of the ET is presented for both the Standard Model and the Chiral
Lagrangian formulated Electro-Weak Theories. It is shown that in electroweak
theories with strongly interacting symmetry breaking sector, the longitudinal
weak-boson scattering amplitude {\it under proper conditions} can be replaced
by the corresponding Goldstone-boson scattering amplitude in which all the
internal weak-boson lines and fermion loops are ignored.
