  We consider a class of impulsive gravitational wave space-times, which
generalize impulsive pp-waves. They are of the form $M=N\times\mathbb{R}^2_1$,
where $(N,h)$ is a Riemannian manifold of arbitrary dimension and $M$ carries
the line element $ds^2=dh^2+ 2dudv+f(x)\delta(u)du^2$ with $dh^2$ the line
element of $N$ and $\delta$ the Dirac measure. We prove a completeness result
for such space-times $M$ with complete Riemannian part $N$.
