  We generalise previous studies on the extension of Goldstone's theorem from
Hermitian to non-Hermitian quantum field theories with Abelian symmetries to
theories possessing a glocal non-Abelian symmetry. We present a detailed
analysis for a non-Hermitian field theory with two complex two component scalar
fields possessing a SU(2)-symmetry and indicate how our finding extend to the
general case. In the PT-symmetric regime and at the standard exceptional point
the Goldstone theorem is shown to apply, although different identification
procedures need to be employed. At the zero exceptional points the Goldstone
boson can not be identified. Comparing our approach, based on the
pseudo-Hermiticity of the model, to an alternative approach that utilises
surface terms to achieve compatibility for the non-Hermitian system, we find
that the explicit forms of the Goldstone boson fields are different.
