  We consider a smooth CR mapping $f$ from a real-analytic generic submanifold
$M$ in $\bC^N$ into $\bC^N$. For $M$ of finite type and essentially finite at a
point $p\in M$, and $f$ formally finite at $p$, we give a necessary and
sufficient condition for $f$ to extend as a holomorphic mapping in some
neighborhood of $p$. In a similar vein, we consider a formal holomorphic
mapping $H$ and give a necessary and sufficient condition for $H$ to be
convergent.
