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Clustering of nodes provides an efficient means of establishing a hierarchical structure in mobile ad hoc networks. In this paper, we introduce two new stability-driven clustering algorithms for pseudolinear highly mobile ad hoc networks such as that of communication between aircraft, ships, trains, and cars on highways. The new algorithms aim at establishing stable clusters, where clusterhead reelection is reduced, and cluster membership periods are increased in the targeted system. The first algorithm is used for scenarios where the position information of nodes is not available, and the second algorithm is aimed at scenarios where position information is available [e.g., nodes are equipped with the Global Positioning System (GPS)]. The algorithms involve dynamic clusterhead election, and the scheme incorporates cluster maintenance to cater to changes in network topology as time progresses. Simulations show that the proposed clustering algorithms provide highly stable clusters with several advantages over previous one-hop clustering schemes.