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Abstract. Ever since scholars in the humanities have studied computer games, the relationship between play and narrative has been a much contested issue. Much dissent stems from incompatible basic assumptions about play and narrative, which, this article argues, can be reconciled by a formalist approach to games and narrative on a structural level. First, event structures and story structures are shown to be central to various theories of narrative. Correlating these findings with Espen Aarseth’s reflections upon nonlinearity, an understanding of narrative revolving around event logic is developed. Building on the theory of games developed by Roger Caillois, the article then develops a model of games in which three layers of structures are governed by three types of rules. The most abstract of these layers arranges game elements in a meta-structure which is based on both ludic and narrative logic. In a final step, nonlinear game structures are explained within this model and categorized in a typology that orders them by the type of agency players can execute.