In this paper, we present an alternative approach to multiple inheritance for typed feature structures. In our approach, a feature structure can be associated with several types coming from different hierarchies (dimensions). In case of multiple inheritance, a type has supertypes from different hierarchies. We contrast this approach with approaches based on a single type hierarchy where a feature structure has only one unique most general type, and multiple inheritance involves computation of greatest lower bounds in the hierarchy. The proposed approach supports current linguistic analyses in constraint-based formalisms like HPSG, inheritance in the lexicon, and knowledge representation for NLP systems. Finally, we show that multi-dimensional inheritance hierarchies can be compiled into a Prolog term representation, which allows to compute the conjunction of two types efficiently by Prolog term unification. 1