Computer vision models based on deep neural networks are proven to be vulnerable to adversarial attacks. Robustness distillation, as a countermeasure, takes both robustness challenges and efficiency challenges of edge models into consideration. However, most existing robustness distillations are data-driven, which can hardly be deployed in data-privacy scenarios. Also, the trade-off between robustness and accuracy tends to transfer from the teacher to the student, and there has been no discussion on mitigating this trade-off in the data-free scenario yet. In this paper, we propose a Data-free Experts-guided Robustness Distillation (DERD) to extend robustness distillation to the data-free paradigm, which offers three advantages: (1) Dual-level adversarial learning strategy achieves robustness distillation without real data. (2) Expert-guided distillation strategy brings a better trade-off to the student model. (3) A novel stochastic gradient aggregation module reconciles the task conflicts of the multi-teacher from a consistency perspective. Extensive experiments demonstrate that the proposed DERD can even achieve comparable results to data-driven methods.