SummaryThe number of endnodes in high‐performance computing systems has grown significantly in the last years. Hence, the interconnection network has become an essential issue as it may end up being the system bottleneck if it is not properly designed. In that sense, the Dragonfly topology has become very popular for interconnecting high‐performance computing systems in the last years because it offers high performance at an affordable cost. However, when using deterministic minimal‐path routing, this topology is not able to offer a high performance under certain traffic conditions. This problem can be solved by using oblivious or adaptive routing. However, there are no congestion management techniques specially tailored to Dragonfly topologies using oblivious or adaptive routing. Note that in congestion situations, the Dragonfly performance may drop because of the head‐of‐line blocking effect. This effect could be even more dangerous in systems where several applications with different priorities coexist. In this work we propose several techniques especially designed for providing differentiated services and congestion management in Dragonfly networks using oblivious or adaptive routing. First, we propose the hierarchical 3‐level queuing queuing scheme, which configures several virtual channels distributed into 3 virtual networks to reduce the head‐of‐line blocking while deadlocks derived from the routing algorithm are prevented. Second, we extend hierarchical 3‐level queuing to provide differentiated services through 2 different solutions. Finally, some experiments are performed to show the benefits obtained by using the proposed techniques.