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All the stable path routing protocols proposed in the literature for mobile ad hoc networks (MANETs) require beacon exchange among the neighbor nodes in order to choose stable links and paths. We propose a beaconless node velocity-based stable path (NVSP) routing protocol for MANETs. NVSP is an on-demand routing protocol that uses the broadcast Route-Request query cycle to discover routes when required. During the propagation of the Route-Request (RREQ) messages, every forwarding node includes its current node velocity information in the RREQs. The bottleneck velocity of a path is the maximum of the velocity of an intermediate node on the path. The destination chooses the path with the smallest bottleneck velocity and sends a Route-Reply (RREP) packet on the chosen path. The lifetime of NVSP routes is 25-35% and 55-75% more than that of the routes chosen by the minimum-hop based Dynamic Source Routing (DSR) protocol in networks of low and high density respectively. The lifetime of routes chosen by NVSP is 60-70% of the route lifetime incurred by the Flow-Oriented Routing Protocol (FORP), the routing protocol observed to determine the sequence of most stable routes in MANETs. On the other hand, the end-to-end delay per data packet and the energy consumed per packet incurred by NVSP are significantly lower than that of FORP and are lower or equal to that incurred for DSR.