Reasoning about terminological cycles of description logics is a hard problem that needs to be solved. Ordered binary decision diagram (OBDD) is a data structure suitable for dealing with large-scale problems since through the diagram Boolean functions can be represented compactly and computed efficiently. In this paper, OBDD is adopted to reason about terminological cycles of description logics. First, for terminological cycles of the description logic εL, with the help of set representation and operation, a property about the greatest simulation relationship on description graphs of terminological cycles is specified and proved. Second, by encoding description graphs of terminological cycles as Boolean functions, an OBDD-based procedure for computing the greatest simulation relationship is proposed, and based on this procedure an algorithm is presented for deciding the subsumption relationship between concepts under the greatest fix-point semantics. Third, based on OBDD, a procedure for calculating all the nodes which can reach cycle paths in a description graph is proposed, and based on this procedure an algorithm for deciding the subsumption relationship under the least fix-point semantics is also presented. Finally, the correctness and time complexity of both algorithms are proved; the computing performance of both algorithms are also demonstrated by a set of experiments. This work provides an effective approach for reasoning about terminological cycles of description logics; it also provides a new case for applying OBDD in the fields of logical reasoning.