  The geodesic as well as the geodesic deviation equation for impulsive
gravitational waves involve highly singular products of distributions
$(\theta\de$, $\theta^2\de$, $\de^2$). A solution concept for these equations
based on embedding the distributional metric into the Colombeau algebra of
generalized functions is presented. Using a universal regularization procedure
we prove existence and uniqueness results and calculate the distributional
limits of these solutions explicitly. The obtained limits are regularization
independent and display the physically expected behavior.
