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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 over(su, ̂) ( N )K and over(sp, ̂) ( n )k, and of level-rank dual twisted D-branes of over(su, ̂) ( 2 n + 1 )2 k + 1. The analysis of level-rank duality of twisted D-branes of over(su, ̂) ( 2 n + 1 )2 k + 1 is facilitated by their close relation to untwisted D-branes of over(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. © 2006 Elsevier B.V. All rights reserved.