  A holomorphic mapping $H$ between two real-analytic CR manifolds $M$ and $M'$
is said to be locally rigid if any other holomorphic map $F\colon M \to M'$
which is close enough to $H$ is obtained by composing $H$ with suitable
automorphisms of $M$ and $M'$. With the aim of reducing the local rigidity
problem to a linear one, we provide sufficient infinitesimal conditions.
Furthermore we study some topological properties of the action of the
automorphism group on the space of nondegenerate mappings from $M$ to $M'$.
