Emerging networked systems become increasingly flexible and “reconfigurable”. This introduces an opportunity to adjust networked systems in a demand-aware manner, leveraging spatial and temporal locality in the workload for online optimizations. However, it also introduces a tradeoff: while more frequent adjustments can improve performance, they also entail higher reconfiguration costs. This paper initiates the formal study of linear networks which self-adjust to the demand in an online manner, striking a balance between the benefits and costs of reconfigurations. We show that the underlying algorithmic problem can be seen as a distributed generalization of the classic dynamic list update problem known from self-adjusting datastructures: in a network, requests can occur between node pairs. This distributed version turns out to be significantly harder than the classical problem in generalizes. Our main results are a Ω(log n) lower bound on the competitive ratio, and a (distributed) online algorithm that is O(log n)- -competitive if the communication requests are issued according to a linear order.