  An algebraic $\Gamma$-action is an action of a countable group $\Gamma$ on a
compact abelian group $X$ by continuous automorphisms of $X$. We prove that any
expansive algebraic action of a finitely generated nilpotent group $\Gamma$ on
a connected group $X$ is ergodic. We also show that this result does not hold
for actions of polycyclic groups.
