Despite some promising early approaches, neural networks have by now received comparatively little attention as a machine learning model for robust, corpus-based anaphor resolution. The work presented in this paper is intended to fill the apparent gap in research. Based on a hybrid algorithm that combines manually knowledge-engineered antecedent filtering rules with machine-learned preference criteria, it is investigated what can be achieved by employing backpropagation networks for the corpus-based acquisition of preference strategies for pronoun resolution. Thorough evaluation will be carried out, thus systematically addressing the numerous experimental degrees of freedom, among which are sources of evidence (features, feature vector signatures), training data generation settings, number of hidden layer nodes, and number of training epochs. According to the evaluation results, the neural network approach performs at least similar to a decision-tree-based ancestor system that employs the same general hybrid strategy.