Computing least common subsumers (lcs) and most specific concepts (msc) are inference tasks that can be used to support the „bottom up” construction of knowledge bases for KR systems based on description logic. For the description logic ALN, the msc need not always exist if one restricts the attention to acyclic concept descriptions. In this paper, we extend the notions lcs and msc to cyclic descriptions, and show how they can be computed. Our approach is based on the automata-theoretic characterizations of fixed-point semantics for cyclic terminologies developed in previous papers. / An abridged version of this technical report has been published at KI'98.