Background: Neighbor-Net is a novel method for phylogenetic analysis that is currently being widely used in areas such as virology, bacteriology, and plant evolution. Given an input distance matrix, Neighbor-Net produces a phylogenetic network, a generalization of an evolutionary or phylogenetic tree which allows the graphical representation of conflicting phylogenetic signals. Results: In general, any network construction method should not depict more conflict than is found in the data, and, when the data is fitted well by a tree, the method should return a network that is close to this tree. In this paper we provide a formal proof that Neighbor-Net satisfies both of these requirements so that, in particular, Neighbor-Net is statistically consistent on circular distances. 1 Background Phylogenetics is concerned with the construction and analysis of evolutionary or phylogenetic trees and networks to understand the evolution of species, populations and individuals [1]. Neighbor-Net is ...