  We define the class of Haken $n$--manifolds as a generalisation of Haken
3--manifolds. We prove that the interior of the universal covering of a Haken
$n$--manifold is $\RR^n$, which generalises a result of Waldhausen. The
techniques used allow us to provide a new proof of Waldhausen's universal cover
theorem for Haken 3--manifolds.
