Flubs are consolidation and dissemination points in many-to-many flow networks. Flub location problem is to locate hubs among available nodes and allocate non-hub nodes to these hubs. The mainstream hub location studies focus on optimal decisions of one decision-maker with respect to some objective(s) even though the markets that benefit hubbing are oligopolies. Therefore, in this paper, we propose a competitive hub location problem where the market is assumed to be a duopoly. Two decision-makers (or firms) sequentially decide locations of their hubs and then customers choose one firm with respect to provided service levels. Each decision-maker aims to maximize his/her own market share. We propose two problems for the leader (former decision-maker) and follower (latter decision-maker): (r vertical bar X-p)hub - medianoid and (r vertical bar p)hub - cent roid problems, respectively. Both problems are proven to be NP-complete. Linear programming models are presented for these problems as well as exact solution algorithms for the (r vertical bar p)hub - centroid problem. The performance of models and algorithms are tested by computational analysis conducted on CAB and TR data sets. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.