  We investigate the geodesics in the entire class of nonexpanding impulsive
gravitational waves propagating in an (anti-)de Sitter universe using the
distributional form of the metric. Employing a 5-dimensional embedding
formalism and a general regularisation technique we prove existence and
uniqueness of geodesics crossing the wave impulse leading to a completeness
result. We also derive the explicit form of the geodesics thereby confirming
previous results derived in a heuristic approach.
