There is currently considerable interest among computational linguists in grammatical formalisms with highly restricted generative power. This paper concerns the relationship between the class of string languages generated by several such formalisms viz. Combinatory Categorial Grammars, Head Grammars, Linear Indexed Grammars and Tree Adjoining Grammars. Each of these formalisms is known to generate a larger class of languages than Context-Free Grammars. The four formalisms under consideration were developed independently and appear superficially to be quite different from one another. The result presented in this paper is that all four of the formalisms under consideration generate exactly the same class of string languages. 1 Introduction There is currently considerable interest among computational linguists in grammatical formalisms with highly restricted generative power. This is based on the argument that a grammar formalism should not merely be viewed as a notation, but as part o...