  Let $\clX$ a projective stack over an algebraically closed field $k$ of
characteristic 0. Let $\clE$ be a generating sheaf over $\clX$ and $\clO_X(1)$
a polarization of its coarse moduli space $X$. We define a notion of pair which
is the datum of a non vanishing morphism $\Gamma\otimes\clE\to \clF$ where
$\Gamma$ is a finite dimensional $k$ vector space and $\clF$ is a coherent
sheaf over $\clX$. We construct the stack and the moduli space of semistable
pairs. The notion of semistability depends on a polynomial parameter and it is
dictated by the GIT construction of the moduli space.
