African languages provide some challenging cases for the standard linguistic theories, because they show striking cases of what I would call synchronic grammaticalization or transcategorial functioning: a same linguistic unit is used synchronically in different syntactic categories, such as ginnaaw in Wolof which can be used as a noun (“ the back ”), as a preposition (“ behind ” or “ excepted ”) or as a subordinating conjunction with the meaning of (causal) “ since ”. As shown by Heine  Kilian-Hatz (1994), the semantic and morphosyntactic variation of some items can be extraordinary, as for the morpheme t in Baka which may behave like a preposition, an auxiliary, a coordinating or subordinating conjunction, and is associated with a number of different domains of grammatical functions such as case marking, subordination, diathesis, predication, derivation, tense-aspect-modality. These cases of transcategorial functioning or “ polygrammaticalization ” (Craig 1991) are not restricted to African languages (cf. Craig 1991 on Rama), and actually crosslinguistically widespread but more or less frequent depending on the languages. The linguistic analysis of such cases raise up some important theoretical questions: how can we account for the semantic and syntactic variation while maintaining the unity of the morpheme? Are the transcategorial morphemes instances of fuzzy categories? Can we distinguish different types of transcategorial functioning and, if so, correlate them with the language’s typological structures? Based on the analysis of the Wolof ginnaaw, I will show that transcategorial functioning can be understood as a fractal property of language, allowing an optimization of the system, and present the functional model of « fractal grammar » (Robert 2003a and 2004). In fact, ginnaaw's synchronic uses across three syntactic categories can be described as a common semantic structure active on three different syntactic levels. This transcategorial functioning is then analyzed in terms of fractals. Objects are said to be 'fractals' when they contain both « scale invariance » (a similar structure appears on different scales) and « scale properties »: each scale has specific properties so that there is no strict identity between the structure’s various avatars at each level (we have an analogic structure). In the same way, we can say that with ginnaaw a similar semantic structure applies at different scales (the linguistic 'scale' is the syntactic 'level' at which the unit functions) and that each syntactic level (or scale) presents 'scale properties' which explain the semantic variation, including the argumentative values of this morpheme at the discourse level. Discourse-based transcategoriality appears then to proceed from the same mechanisms but activating the specific (scale) properties of the discourse level. Combining scale invariance and scale properties, this dynamic model can account for the transcategorial functioning of linguistic morphemes by relating semantic variation to syntax: the variation of the syntactic scope of the morpheme produces its polysemy. Eventually, I will draw a preliminary typological sketch of transcategoriality, aiming at explaining why this transcategorial functioning is attested with various degrees across languages (cf Robert 2003b). References Craig Colette G., 1991, Ways to Rama : A case study in polygrammaticalization. In Elisabeth C. Traugott and Bernd Heine eds, Approaches to grammaticalization, Volume 2. Typological studies in language 19. Amsterdam and Philadelphia, John Benjamins : 455-492. Heine Bernd  Christa Kilian-Hatz, 1994, Polysemy in African languages: An example from Baka, Thomas Geider  Raimund Kastenholz (eds), Sprachen un Sprachzeugnisse in Afrika. Eine Sammlung philologischer Beiträgen Wilhelm J.G. Möhlig zum 60 Geburtstag zugeeignet, Köln, Rudiger Köppe Verlag. Robert, Stéphane. 2003a, « Polygrammaticali¬sation, gram¬maire fractale et propriétés d'échelle » ; in S. Robert (éd.), Perspectives synchroniques sur la grammaticalisation: Polysémie, , transcatégorialité et échelles syntaxiques, Collection Afrique et Langage n°5, Editions Peeters, Louvain, 85-120. Robert, Stéphane. 2003b, « Vers une typologie de la transcatégorialité », in S. Robert (éd.), Perspectives synchroniques sur la grammaticalisation: Polysémie, transcatégorialité et échelles syntaxiques, Collection Afrique et Langage n°5, Editions Peeters, Louvain, 255-270. Robert, Stéphane. 2004 “The challenge of polygrammaticalization for linguistic theory: fractal grammar and transcategorial functioning”, in Zygmunt Frajzyngier, Adam Hodges and David S. Rood eds., Linguistic Diversity and Language Theories [Studies in language companion series 72], J. Benjamins: Amsterdam / Philadelphia, 119-142.