  We study compact locally homogeneous plane waves. Such a manifold is a
quotient of a homogeneous plane wave $X$ by a discrete subgroup of its isometry
group. This quotient is called standard if the discrete subgroup is contained
in a connected subgroup of the isometry group that acts properly cocompactly on
$X$. We show that compact quotients of homogeneous plane waves are
``essentially" standard; more precisely, we show that they are standard or
`semi-standard'. We find conditions which ensure that a quotient is not only
semi-standard but even standard. As a consequence of these results, we obtain
that the flow of the parallel isotropic vector field of a compact locally
homogeneous plane wave is equicontinuous.
