This thesis interprets literary allusions in three major Babylonian narrative poems: Anzû, Enūma Eliš, and Erra and Išum. The use of the term 'intertextuality' recognises that these readings do not necessarily attempt to reconstruct what the authors were thinking, but are based empirically on what can be found in the text, and that multiple interpretations are possible. The methodology used has been drawn from scholarship on Latin and Greek literature. The aim is not only to identify relationships to other poems but also to consider what these mean, closely analysing the similarities and differences in order to draw out each allusion's full significance. A wide variety of allusive techniques have been found, showing great depth, complexity, and sophistication. Chapter One finds that Anzû alludes to Lugal-e, Labbu, Atraḫasīs, The Return of Lugalbanda, and balaĝ-laments. Chapter Two explores allusions in Enūma Eliš to Anzû, which depict Marduk as the new Ninurta. Chapter Three analyses allusions in Enūma Eliš to Atraḫasīs, which contribute to Marduk's superseding of Enlil. Chapter Four studies allusions in Enūma Eliš to Lugal-e, finding that Marduk's restoration of order after the battle owes as much to Ninurta's precedent as does the battle itself. Chapter Five examines allusions in Erra and Išum to Anzû and Lugal-e which present Išum as a new Ninurta, and Erra as a chaotic Anzû figure. Chapter Six considers allusions in Erra to Enūma Eliš, Atraḫasīs, and Gilgameš, which work together to show the cosmic order unravelling. In many of these examples, the relationship is a competitive one, where Anzû, Enūma Eliš, and Erra each conspicuously out-do the protagonists of the poems which came before them. Chapter Seven finds that the underlying structure of Erra and Išum parallels that of The Lamentation over the Destruction of Sumer and Ur, and argues it is deliberate, which raises intriguing questions about the continuity of Sumerian city laments after the Old Babylonian period. Thus it is demonstrated that allusion is a vital part of Akkadian poetics, and that close-reading Akkadian texts unlocks deeper meaning within them.