  We investigate a class of impulsive gravitational waves which propagate
either in Minkowski or in the (anti-)de Sitter background. These waves are
constructed as impulsive members of the Kundt class $P(\Lambda)$ of
non-twisting, non-expanding type N solutions of vacuum Einstein equations with
a cosmological constant $\Lambda$. We show that the only non-trivial waves of
this type in Minkowski spacetime are impulsive pp-waves. For $\Lambda\not=0$ we
demonstrate that the canonical subclasses of $P(\Lambda)$, which are
invariantly different for smooth profiles, are all locally equivalent for
impulsive profiles. Also, we present coordinate system for these impulsive
solutions which is explicitly continuous.
