  We introduce Koszul modules associated with (graded) Kac-Moody Lie algebras.
We provide a precise criterion for when these modules are of finite length. As
an exemplary application we deduce a bound on the dimension of the second
graded component for a certain class of graded Kac-Moody Lie algebras. We also
provide an exact description of all nilpotent Kac-Moody Koszul modules.
