  We study D-branes in the Nappi-Witten model, which is a gauged WZW model
based on (SL(2,R) x SU(2)) / (U(1) x U(1)). The model describes a four
dimensional space-time consisting of cosmological regions with big bang/big
crunch singularities and static regions with closed time-like curves. The aim
of this paper is to investigate by D-brane probes whether there are pathologies
associated with the cosmological singularities and the closed time-like curves.
We first classify D-branes in a group theoretical way, and then examine DBI
actions for effective theories on the D-branes. In particular, we show that
D-brane metric from the DBI action does not include singularities, and wave
functions on the D-branes are well behaved even in the presence of closed
time-like curves.
