  The Siklos class of solutions of Einstein's field equations is investigated
by analytical methods. By studying the behaviour of free particles we reach the
conclusion that the space-times represent exact gravitational waves propagating
in the anti-de Sitter universe. The presence of a negative cosmological
constant implies that the 'background' space is not asymptotically flat and
requires a 'rotating' reference frames in order to fully simplify and view the
behaviour of nearby test particles. The Kaigorodov space-time, which is the
simplest representative of the Siklos class, is analyzed in more detail. It is
argued that it may serve as a 'cosmological' analogue of the well-known
homogeneous pp-waves in the flat universe.
