Adequateness is one of the most important issues in knowledge representation and reasoning. Roughly speaking, a reasoning system is adequate if it solves simpler problems faster than more diicult ones, where simplicity is measured with respect to all available reasoning systems. It has been shown recently that adequateness implies massive parallelism and, hence, we should be interested in reasoning problems which admit an optimal or eecient parallel computational model. Such problems must be in P and must not be the hardest problems in P unless P = NC. Terminological reasoning systems were developed to provide fast and tractable reasoning services and, in particular, to compute the subsumption relation between concept descriptions or, equivalently, to determine the unsatissability of a concept description. In this paper we develop an eecient parallel algorithm for checking unsatissability for the AL concept language and prove its correctness and completeness.