  In an SU(2) gauge theory, if the gauge bosons turn out to be degenerate after
spontaneous symmetry breaking, obviously these mass terms are invariant under a
global SU(2) symmetry that is unbroken. The pure gauge terms are also invariant
under this symmetry. This symmetry is called the {\em custodial symmetry} (CS).
In $\rm SU(2)\times U(1)$ gauge theories, CS implies a mass relation between
the $W$ and the $Z$ bosons. The Standard Model (SM), as well as various
extensions of it in the scalar sector, possess such a symmetry. In this paper,
we critically examine the notion of CS and show that there may be three
different classes of CS, depending on the gauge couplings and self-couplings of
the scalars. Among old models that preserve CS, we discuss the Two-Higgs
Doublet Model and the one doublet plus two triplet model by Georgi and
Machacek. We show that for two-triplet extensions, the Georgi-Machacek model is
not the most general possibility with CS. Rather, we find, as the most general
extension, a new model with more parameters and hence a richer phenomenology.
Some of the consequences of this new model have also been discussed.
