The introduction of robust optimisation has pushed the state-of-the-art in defending against adversarial attacks. Notably, the state-of-the-art projected gradient descent (PGD)-based training method has been shown to be universally and reliably effective in defending against adversarial inputs. This robustness approach uses PGD as a reliable and universal "first-order adversary". However, the behaviour of such optimisation has not been studied in the light of a fundamentally different class of attacks called backdoors. In this paper, we study how to inject and defend against backdoor attacks for robust models trained using PGD-based robust optimisation. We demonstrate that these models are susceptible to backdoor attacks. Subsequently, we observe that backdoors are reflected in the feature representation of such models. Then, this observation is leveraged to detect such backdoor-infected models via a detection technique called AEGIS. Specifically, given a robust Deep Neural Network (DNN) that is trained using PGD-based first-order adversarial training approach, AEGIS uses feature clustering to effectively detect whether such DNNs are backdoor-infected or clean. In our evaluation of several visible and hidden backdoor triggers on major classification tasks using CIFAR-10, MNIST and FMNIST datasets, AEGIS effectively detects PGD-trained robust DNNs infected with backdoors. AEGIS detects such backdoor-infected models with 91.6% accuracy (11 out of 12 tested models), without any false positives. Furthermore, AEGIS detects the targeted class in the backdoor-infected model with a reasonably low (11.1%) false positive rate. Our investigation reveals that salient features of adversarially robust DNNs could be promising to break the stealthy nature of backdoor attacks.