Diffusion- and flow-based models have advanced Real-world Image Super-Resolution (Real-ISR), but their multi-step sampling makes inference slow and hard to deploy. One-step distillation alleviates the cost, yet often degrades restoration quality and removes the option to refine with more steps. We present Mean Flows for Super-Resolution (MFSR), a new distillation framework that produces photorealistic results in a single step while still allowing an optional few-step path for further improvement. Our approach uses MeanFlow as the learning target, enabling the student to approximate the average velocity between arbitrary states of the Probability Flow ODE (PF-ODE) and effectively capture the teacher's dynamics without explicit rollouts. To better leverage pretrained generative priors, we additionally improve original MeanFlow's Classifier-Free Guidance (CFG) formulation with teacher CFG distillation strategy, which enhances restoration capability and preserves fine details. Experiments on both synthetic and real-world benchmarks demonstrate that MFSR achieves efficient, flexible, and high-quality super-resolution, delivering results on par with or even better than multi-step teachers while requiring much lower computational cost.