The compression of Generative Adversarial Networks (GANs) has lately drawn attention, due to the increasing demand for deploying GANs into resource-constrained (mobile) devices for numerous applications such as image translation, enhancement and editing. However, compared to the substantial efforts to compressing other deep models, the research on compressing GANs (usually the generators) remains at its infancy stage. Existing GAN compression algorithms are heavily limited to handling specific GAN architectures and losses. Inspired by the recent success of AutoML in deep compression, we introduce AutoML to GAN compression for the first time and develop an Auto-GAN-Distiller (AGD) framework. Starting with a specifically designed efficient search space, AGD performs an end-to-end discovery for new efficient generators, given the target computational resource constraints. The search is guided by the original GAN model via knowledge distillation, therefore fulfilling the compression of the latter. AGD is fully automatic, standalone (i.e., needing no trained discriminators), and generically applicable to various GAN models. We evaluate AGD in two representative GAN tasks: image translation and super resolution. Without bells and whistles, AGD yields remarkably lightweight yet more competitive compressed models, that largely outperform existing alternatives. All codes and pre-trained models will be released upon acceptance.