  The doublet-triplet splitting problem is perhaps the most problematic aspect
of supersymmetric grand unified theories. It can be argued that the most
natural reason for the Higgs doublets to be light is that they are
pseudo-Goldstone bosons associated with the spontaneous breakdown of an
accidental global symmetry. In this paper we discuss the possibility of
implementing this idea in the SU(6) model of refs. \cite{Zur,Bar2,Bar3,Bar4}.
We show that although it is simple to generate an accidental symmetry of the
renormalizable terms of the potential, it is quite difficult to construct a
model which allows for the preservation of the accidental symmetry in the
nonrenormalizable terms. We summarize the constraints on such models and then
give three different ways to construct a superpotential where the dangerous
mixing terms are sufficiently suppressed even in the presence of
nonrenormalizable operators. With these examples we demonstrate the existence
of consistent models implementing the Higgs as pseudo-Goldstone boson scheme.
We extend one of the three examples to include fermion masses. We also show
that when restricted to regular group embeddings the only possible models
without light triplets are trivial generalizations of the SU(6) model we
consider.
