  We study the structure of the supersymmetric moduli spaces of ${\cal N}=1$
and ${\cal N}=2$ supergravity theories in $AdS_4$ backgrounds. In the ${\cal
N}=1$ case, the moduli space cannot be a complex submanifold of the K\"ahler
field space, but is instead real with respect to the inherited complex
structure. In ${\cal N}=2$ supergravity the same result holds for the vector
multiplet moduli space, while the hypermultiplet moduli space is a K\"ahler
submanifold of the quaternionic-K\"ahler field space. These findings are in
agreement with AdS/CFT considerations.
