Most current linguistic theories give lexical accounts of several phenomena that used to be considered purely syntactic. The information put in the lexicon is thereby increased in both amount and complexity: see, for example, lexical rules in LFG (Kaplan and Bresnan, 1983), GPSG (Gazdar, Klein, Pullum and Sag, 1985), HPSG (Pollard and Sag, 1987), Combinatory Categorial Grammars (Steedman, 1987), Karttunen's version of Categorial Grammar (Karttunen 1986, 1988), some versions of GB theory (Chomsky 1981), and Lexicon-Grammars (Gross 1984). We would like to take into account this fact while defining a formalism. We therefore explore the view that syntactical rules are not separated from lexical items. We say that a grammar is lexicalized (Schabes, AbeilK and Joshi, 1988) if it consists of: (1) a finite set of structures each associated with lexical items; each lexical item will be called the anchor of the corresponding structure; the structures define the domain of locality over which constraints are specified; (2) an operation or operations for composing the structures. The notion of anchor is closely related to the word associated with a functor-argument category in Categorial Grammars. Categorial Grammar (as used for example by Steedman, 1987) are 'lexicalized' according to our definition since each basic category has a lexical item associated with it.