Learnt deep neural networks for image super-resolution fail easily if the assumed degradation model in training mismatches that of the real degradation source at the inference stage. Instead of attempting to exhaust all degradation variants in simulation, which is unwieldy and impractical, we propose a novel adversarial neural degradation (AND) model that can, when trained in conjunction with a deep restoration neural network under a minmax criterion, generate a wide range of highly nonlinear complex degradation effects without any explicit supervision. The AND model has a unique advantage over the current state of the art in that it can generalize much better to unseen degradation variants and hence deliver significantly improved restoration performance on real-world images.