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In this paper, we consider the problem of unbalanced energy consumption for nodes in wireless sensor networks (WSN). Current routing protocols divide the network into clusters and route data packets by electing cluster heads, but ineffective network energy utilization leads to the death of nodes very soon. We show that the behavior of sensor networks becomes very unstable once the first node dies. We propose NSEEAR - network stability enhancement by energy aware routing, an adaptive routing protocol which leads to a better energy utilization of the network to prolong its stability period (the time interval before the death of the first node) and the significant network lifetime (the time interval before half of the network is dead) which is crucial for many sensing applications in which the feedback from the network should be reliable. NSEEAR organizes the network into concentric tiers around the base station and routes aggregated data packets by forwarding them from one tier to another in the direction of the base station. Relaying nodes are elected by considering their distance from the transmitting node and the base station, as well as their residual energy. We evaluate NSEEAR through analysis and simulations and show that NSEEAR results in much longer stability periods compared to those obtained by the current clustering protocols.