  The category of finite dimensional (type 1) representations of a quantum
affine algebra $U_q(\hat{{\mathfrak g}})$ is not semisimple. However, as any
abelian category with finite-length objects, it admits a unique decomposition
into a direct sum of indecomposable subcategorie (blocks). We define the
elliptic central character of a finite dimensional (type 1) representation of
$U_q(\hat{{\mathfrak g}})$. Then we show that the block decomposition of this
category is paramentrized by these elliptic central characters.
