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Critical current densities (Jc) and irreversibility fields (Birr) of high-Tc superconductors AuBa2Can−1CunO2n+3 [Au-12(n−1)n, n=3,4] prepared under high pressure were determined from the hysteresis in DC magnetization loop. Both the Jc and Birr values of the Au-1234 phase were larger than those of Hg- and Bi-based cupurate superconductors, but smaller than those of the Y-123 superconductor. This result suggests that the electronic structure of Au-1234 is less anisotropic compared with the Hg- and Bi-phases. The Au-1223 phase showed very small Jc values corresponding to its small superconducting volume fraction. [Copyright &y& Elsevier]