  The core of an module is the intersection of all its reductions. The main
result asserts that the core of a finitely generated, torsion-free, integrally
closed module over a two dimensional regular local ring is the product of the
module and the adjoint of an ideal. This generalizes the fundamental formula
for the core of an integrally closed ideal in a two-dimensional regular local
ring due to Huneke and Swanson. As an application, we show that for integrally
closed modules $M$ and $N$ over a two-dimensional regular local ring with
$M\subset N$ and $M^{**}=N^{**}$, the core of $M$ is contained in the core of
$N$.
