By using a highly sensitive homemade AC magnetic susceptibility technique, the magnetic flux penetration has been measured in YBa2Cu3O7 - δ single crystals with giant screw dislocations (having the structure of the Archimedean spirals) exhibiting a = 3 spiral turnings, the pitch b = 18.7 μm and the step height c = 1.2 nm (the last parameter is responsible for creation of extended weak-link structure around the giant defects). The magnetic field applied parallel to the surface enters winding around the weak-link regions of the screw in the form of the so-called spiral Josephson fluxons characterized by the temperature dependent pitch bf(T). For a given temperature, a stabilization of the fluxon structure occurs when bf(T) matches b (meaning an optimal pinning by the screw dislocations) and manifests itself as a pronounced low-field peak in the dependence of the susceptibility on magnetic field (applied normally to the surface) in the form resembling the high-field (Abrikosov) fishtail effect. © Pleiades Publishing, Inc., 2010.