  Level-rank duality of untwisted and twisted D-branes of WZW models is
explored. We derive the relation between D0-brane charges of level-rank dual
untwisted D-branes of su(N)_K and sp(n)_k, and of level-rank dual twisted
D-branes of su(2n+1)_2k+1. The analysis of level-rank duality of twisted
D-branes of su(2n+1)_2k+1 is facilitated by their close relation to untwisted
D-branes of sp(n)_k. We also demonstrate level-rank duality of the spectrum of
an open string stretched between untwisted or twisted D-branes in each of these
cases.
