  We study compactifications of type II theories on SU(2) x SU(2) structure
manifolds to six, five and four spacetime dimensions. We use the framework of
generalized geometry to describe the NS-NS sector of such compactifications and
derive the structure of their moduli spaces. We show that in contrast to SU(3)
x SU(3) structure compactifications, there is no dynamical SU(2) x SU(2)
structure interpolating between an SU(2) structure and an identity structure.
Furthermore, we formulate type II compactifications on SU(2) x SU(2) structures
in the context of exceptional generalized geometry which makes the U-duality
group manifest and naturally incorporates the scalar degrees of freedom arising
in the Ramond-Ramond sector. Via this formalism we derive the structure of the
moduli spaces as it is expected from N=4 supergravity.
