Distilled student models in teacher-student architectures are widely considered for computational-effective deployment in real-time applications and edge devices. However, there is a higher risk of student models to encounter adversarial attacks at the edge. Popular enhancing schemes such as adversarial training have limited performance on compressed networks. Thus, recent studies concern about adversarial distillation (AD) that aims to inherit not only prediction accuracy but also adversarial robustness of a robust teacher model under the paradigm of robust optimization. In the min-max framework of AD, existing AD methods generally use fixed supervision information from the teacher model to guide the inner optimization for knowledge distillation which often leads to an overcorrection towards model smoothness. In this paper, we propose an adaptive adversarial distillation (AdaAD) that involves the teacher model in the knowledge optimization process in a way interacting with the student model to adaptively search for the inner results. Comparing with state-of-the-art methods, the proposed AdaAD can significantly boost both the prediction accuracy and adversarial robustness of student models in most scenarios. In particular, the ResNet-18 model trained by AdaAD achieves top-rank performance (54.23% robust accuracy) on RobustBench under AutoAttack.