It has been argued that science is generated and validated through processes of controversy, and that controversies are 'closed' through 'rhetorical' processes of 'enrolment of heterogeneous allies and resources.' It has also been argued that, once a controversy is closed, it is increasingly difficult for the 'losing' position to maintain the plausibility of its views, arguments, and interpretations (words like 'reification,' 'inertia,' and 'institutionalisation' have been used to refer to this). Controversies have shaped neural network research throughout its history, from the 1950s to the 1980s. In this dissertation I analyse the history of neural network research using a 'controversy/rhetorical tactics/enrolment of allies and resources/closure' scheme. I claim that the result is a useful and powerful interpretation of the main developments of the evolution of neural network research. The neural network controversy is especially interesting because it was once (in the late 1960s) closed against neural networks, and twenty years later (in the late 1980s) it was reopened. The history of neural network research can be seen as the history of the closure and reopening of the neural network controversy.