  We study the deformation theory of CR maps in the positive codimensional
case. In particular, we study structural properties of the {\em mapping locus}
$E$ of (germs of nondegenerate) holomorphic maps $H \colon (M,p) \to M'$
between generic real submanifolds $M \subset \mathbb C^N$ and $M' \subset
\mathbb C^{N'}$, defined to be the set of points $p' \in M'$ which admit such a
map with $H(p) = p'$. We show that this set $E$ is semi-analytic and provide
examples for which $E$ posseses (prescribed) singularities.
