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The paper presents a computational model aiming at making the morphological structure of the lexicon emerge from the formal and semantic regularities of the words it contains. The model is purely lexeme-based. The proposed morphological structure consists of (1) binary relations that connect each headword with words that are morphologically related, and especially with the members of its morphological family and its derivational series, and of (2) the analogies that hold between the words. The model has been tested on the lexicon of French using the TLFi machine readable dictionary.