This paper addresses the distributed adaptive security consensus control problem of a class of nonlinear multi-agent systems subject to network decay and intermittent attacks. The network communication is decayed and intermittently attacked by attackers, which may result in loss of transmission effectiveness and communication outage, respectively. A distributed adaptive consensus control strategy is firstly developed to ensure bounded consensus of the nonlinear multi-agent systems in the case of normal networks. Then, a novel adaptive neural network (NN)-based observer is proposed to observe decayed and intermittent transmission signals of networks in such a way to recover the original signals. Based on the adaptive control and NN-based observer schemes, distributed security control strategies are developed to achieve the bounded consensus of the multi-agent systems under the influence of network decay and intermittent attacks. The efficiency of the designed adaptive security control strategies are illustrated by a multiple coupled nonlinear forced pendulum system.