  We extend to twisted spectral triples the fluctuations of the metric, as well
as their gauge transformations. The former are bounded perturbations of the
Dirac operator that arise when a spectral triple is exported between Morita
equivalent algebras; the later are obtained by the action of the unitary
endomorphisms of the module implementing the Morita equivalence. It is shown
that the twisted gauged Dirac operators, previously introduced to generate an
extra scalar field in the spectral description of the standard model of
elementary particles, in fact follow from Morita equivalence between twisted
spectral triples. The law of transformation of the gauge potentials turns out
to be twisted in a natural way. In contrast with the non-twisted case, twisted
fluctuations do not necessarily preserve the self-adjointness of the Dirac
operator. For a self-Morita equivalence, some conditions are obtained in order
to maintain self-adjointness, that are solved explicitly for the minimal twist
of a Riemannian manifold.
