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Below 1 Tesla pinned JF yield j/sub c//spl ap/j/sub cJ//spl les/5/spl middot/10/sup 7/A/cm/sup 2/ with j/sub cJ/ the critical Josephson current. The pinning is due to irregularities in the Josephson junctions (weak links) consisting of insulating seams of finite length and varying width, e.g., grain or twin boundaries. At higher fields Abrikosov fluxons (AF) in single crystalline parts may dominate j/sub c/, where j/sub c/ still has to be carried by strong and weak links in series, i.e., by Josephson fluxons (JF) strongly pinned. In addition, the insulating regions at strong and weak links amount to the largest concentration of insulating material in cuprate superconductors able to pin fluxons. Dynamic properties, like, the strong field and frequency dependencies of the surface impedance or the fast transition from normal-to-superconducting state are solely explainable by fast JF with their low loss insulating cores. Because j/sub c/ is given by a critical amount of dissipation, the viscous dynamics of JF- or AF-sliding along weak links play a critical role in superconductors containing strong or weak links.