  We discuss the causal structure of pp-wave spacetimes using the ideal point
construction outlined by Geroch, Kronheimer, and Penrose. This generalizes the
recent work of Marolf and Ross, who considered similar issues for plane wave
spacetimes. We address the question regarding the dimension of the causal
boundary for certain specific pp-wave backgrounds. In particular, we
demonstrate that the pp-wave spacetime which gives rise to the N = 2
sine-Gordon string world-sheet theory is geodesically complete and has a
one-dimensional causal boundary.
