Beginning with Goldsmith (1976), the phonological tier has a long history in phonological theory to describe non-local phenomena. This paper defines a class of formal languages, the Tier-based Strictly Local languages, which begin to describe such phenomena. Then this class is located within the Subregular Hierarchy (McNaughton and Papert, 1971). It is found that these languages contain the Strictly Local languages, are star-free, are incomparable with other known sub-star-free classes, and have other interesting properties. .
