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We present AMOR, a new scheme for on-demand routing in wireless ad hoc networks. In ad hoc networks, mobile nodes are connected to each other such that the connection pattern changes dynamically with the mobility of nodes. Therefore, classical table driven routing algorithms necessitate updated network state information to be periodically disseminated, and incur significant costs in terms of network utilization, memory, and associated update-processing. In contrast, on-demand routing algorithms do not maintain pre-computed routes and real time route discovery ensues when data traffic needs to be transmitted between a source-destination pair. AMOR employs a modified version of the Dynamic Source Routing protocol to discover multiple node-disjoint paths between a source-destination pair. A key feature of AMOR is that instead of computing minimum-hop paths, it computes paths such that a measure of the 'transmission reliability', namely ETX, between the source-destination pair is optimized. Furthermore, AMOR employs a real time loading algorithm that optimally load balances traffic across multiple paths. The control traffic overhead in AMOR is comparable to that of single-path on-demand protocols. We present analytical throughput results in a simplified AMOR model of a network of multi-radio nodes. We also conduct simulation experiments to study the throughput performance of the AMOR scheme in a network of single-radio nodes. Our results show that AMOR outperforms the traditional dynamic source routing algorithm.