In Web-based social media (blogs, Internet forums, etc.), readers express their opinions by attaching reply comments to articles and understand others' perspectives by reading these comments. On Web forums, users discuss and argue with others via reply comments. Thus, a series of comments may provide new information, particularly about disputes among participants. Unfortunately, current systems for viewing reply comments are primitive; it is hard to follow disputes and their relationships by using such systems. We examine the characteristics of disputes by using reply comments and propose a novel system for automatically detecting disputes and their relationships among a large set of reply comments. This paper defines a dispute section as a series of comments where the dispute index is sufficiently high. The dispute index is determined using an exponential model with three control parameters. Next, the dispute relationship can be defined according to a pair of arguing commenters. The basic concept is to exploit the order of comment posting times and comment writer information when detecting dispute sections because the comments tend to appear in ordered pairs. The proposed system detects dispute sections and visualizes them according to dispute relationships among commenters, enabling users to appreciate the controversial structure of comments. To test the performance of our system, we constructed a dataset containing comment sequences associated with 40 articles collected from an Web forum. We constructed the set of dispute comments manually. We found that the detection accuracy of our system for disputes and their relationships were 83% and 78% on average. Copyright © 2012 John Wiley & Sons, Ltd.