The last decade of basic research in the area of Description Logics (DL) has created a stable theory, efficient inference procedures, and has demonstrated a wide applicability of DL to knowledge representation and reasoning. The success of DL in the semantic web and the distributed nature of the last one inspired recently a proposal of Distributed DL framework (DDL). DDL is composed of a set of stand alone DLs pairwise interrelated with each other via collection of bridge rules. In this paper, we investigate the reasoning mechanisms in DDL and introduce a tableau-based reasoning algorithm for DDL, built on the top of the state of the art tableaux reasoners for DL. We also describe a first prototype implementation of the proposed algorithm.