The purpose of this paper is to present a grammatical formalism that extends context-free grammars and aims at being a convincing challenger as a syntactic base for various tasks, especially in natural language processing. These grammars are powerful, they strictly include mildly context-sensitive languages, while staying computationally tractable, since sentences are parsed in polynomial time. Moreover, this formalism allows a form of modularit- y which may lead to the design of libraries of reusable generic grammatical components. And, last, it can act as a syntactic backbone upon which decoratio- ns from other domains (say feature structures) can be grafted.