Terminological knowledge representation formalisms in the tradition of kl-oneenable one to de ne the relevant concepts of a problem domain and their interaction in a structured and well-formed way. Recently, M. Schmidt-Schau and G. Smolka proposed a new methodology for constructing sound and complete inference algorithms for terminological logics. The consistency test of assertions is the basis for all terminological reasoning services. We propose constraint handling rules (CH rules) as an implementation language for terminological reasoning. CH rulesare a exible means to implement `user-de ned' constraints on top of existing host languages like Prolog and Lisp. The implementation results in a natural combination of three layers: (i) a constraint layer that reasons in well-understood domains such as rationals or nite domains, (ii) a terminological layer providing a tailored, validated vocabulary on which (iii) the application layer can rely. As an application example, a con guration problem is modeled. The exibility of the approach will be illustrated by extending the formalism, its implementation and the example with attributes, a new quanti er and concrete domains. Preliminary versions of this report were presented at the Workshop on Principles and Practice of Constraint Programming, Newport, Rhode Island, USA, April 1993 and as Technical Report ECRC CORE93-13, February 1993. Thom Fr uhwirth is partially supported by ESPRIT Project 5291 CHIC. This work was done while Philipp Hanschke worked at DFKI, Postfach 2080, 67608 Kaiserslautern, Germany, and was supported by BMFT Projects ARC-TEC (Grant ITW 8902 C4) and IMCOD/VEGA (Grant 413 5839 ITW 9304/3).