  We construct coarse moduli spaces for `Brill-Noether pairs'. Such a pair
consists of a torsion-free sheaf $E$ over an algebraic curve $X$ and a vector
subspace $\Lambda$ of its space of sections $H^0(E)$. The construction works
for an arbitrary singular curve $X$ of pure dimension and for all values of the
positive rational parameter $\alpha$ occurring in the stability condition.
(Hard copies available on request.)
