  An abelian Krull-Schmidt category is said to be uniserial if the isomorphism
classes of subobjects of a given indecomposable object form a linearly ordered
poset. In this paper, we classify the hereditary uniserial categories with
Serre duality. They fall into two types: the first type is given by the
representations of the quiver A_n with linear orientation (and infinite
variants thereof), the second type by tubes (and an infinite variant). These
last categories give a new class of hereditary categories with Serre duality,
called big tubes.
