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In recent years, neuromorphic computing systems (NCS) have gained popularity in accelerating neural network computation because of their high energy efficiency. The known vulnerability of neural networks to adversarial attack, however, raises a severe security concern of NCS. In addition, there are certain application scenarios in which users have limited access to the NCS. In such scenarios, defense technologies that require changing the training methods of the NCS, e.g., adversarial training become impracticable. In this work, we propose AdverQuil – an efficient adversarial detection and alleviation technique for black-box NCS. AdverQuil can identify the adversarial strength of input examples and select the best strategy for NCS to respond to the attack, without changing structure/parameter of the original neural network or its training method. Experimental results show that on MNIST and CIFAR-10 datasets, AdverQuil achieves a high efficiency of 79.5 - 167K image/sec/watt. AdverQuil introduces less than 25% of hardware overhead, and can be combined with various adversarial alleviation techniques to provide a flexible trade-off between hardware cost, energy efficiency and classification accuracy.