The temperature‐independent residual surface resistanceRresof high‐Q‐superconducting resonators is up till now not well understood. Experiments in lead‐plated copper cavities and massive niobium cavities (&ngr;≃GHz) have shownRres∝&ohgr;1.8±0.2, which excludes normal conducting regions as a cause for the rf losses. An explanation is presented which can describe the observed dependencies on frequency and on surface treatment: The losses are caused by the generation of phonons in fissured surfaces by locally excited rf fields. These losses are temperature independent, giveRres∝&ohgr;2and can also explain the observed mode dependence in lead‐plated copper cavities.