  We develop a several variables analog of the Jordan blocks of the Hardy space
$H^2(\mathbb{D})$. In this consideration, we obtain a complete characterization
of the doubly commuting quotient modules of the Hardy module
$H^2(\mathbb{D}^n)$. We prove that a quotient module $\clq$ of
$H^2(\mathbb{D}^n)$ ($n \geq 2$) is doubly commuting if and only if \[\clq =
\clq_{\Theta_1} \otimes \cdots \otimes \clq_{\Theta_n},\]where each
$\clq_{\Theta_i}$ is either a one variable Jordan block
$H^2(\mathbb{D})/\Theta_i H^2(\mathbb{D})$ for some inner function $\Theta_i$
or the Hardy module $H^2(\mathbb{D})$ on the unit disk for all $i = 1, \ldots,
n$. We say that a submodule $\cls$ of $H^2(\mathbb{D}^n)$ is a co-doubly
commuting if the quotient module $H^2(\mathbb{D}^n)/\cls$ is doubly commuting.
We obtain a Beurling like theorem for the class of co-doubly commuting
submodules of $H^2(\mathbb{D}^n)$. We prove that a submodule $\cls$ of
$H^2(\mathbb{D}^n)$ is co-doubly commuting if and only if \[\cls =
\mathop{\sum}_{i=1}^m \Theta_i H^2(\mathbb{D}^n),\]for some integer $m \leq n$
and one variable inner functions $\{\Theta_i\}_{i=1}^m$.
