a neighborhood of $p$ in $N$ there exists $\W_v$, a wedge of direction $v$ whose edge contains $N$ such that $f$ has a holomorphic extension to $\W_v$. In this paper, we shall study the case where $N$ is not totally real, that is we consider CR submanifolds of $\C^L$ given by $N=\{(\n,h(\n))\}$ where $\n$ is generic in $\C^{k+m}$ of CR dimension $k>0$. We say that a CR distribution extends holomorphically to a wedge $\W$ if there exists a holomorphic function $F$ in $W$ such that the boundary value of $F$ on $N$ is $f$, i.e $<f,\varphi>=
\lim_{\lambda \to 0^+} \int_{N}F(x+\lambda v)\varphi(x)dx$ for any $v \in  \W$.

\[th\] Let $N=\{(\n,h(\n))\} $ be a smooth ($\CC^{\infty})$ non generic CR submanifold of $\C^{k+1}\times \C^n$ such that $\n \subset \C^{k+1}$ is a hypersurface. If $f$ is a CR distribution on $N$ then for any $p \in
N$ and any $v$ complex transversal to $N$ at $p$, there exists a wedge $\W$ of direction $v$ whose edge contains a neighborhood of $p$ in $N$ and $F\in \O(\W)$ such that the boundary value of $F$ on $N$ is $f$.

We obtain some extension results for arbitrary $\n$ for decomposable CR distributions. Since the CR structure of 