H-2 permeation hysteresis has been observed during cycling of a 3 mu m thick supported PdCu membrane with similar to 50 atom % Pd through the fcc/bcc (face-centered cubic/body-centered cubic) miscibility gap between 723 and 873 K. Structural investigations after annealing of membrane fragments under H-2 at 823 K reveal retardation of the fcc(H) -> bcc(H) transition, which is attributed to the occurrence of metastable hydrogenated fee PdCu(H) phases. The H-2 flux at 0.1 MPa H-2 pressure difference in the well-annealed bcc single phase regime below 723 K can be described by J(H2) = (1.3 +/- 0.2) mol.m(-2).s(-1) exp[(-11.1 +/- 0.6) kJ.mol(-1)/(RT)] and that in the fcc single phase regime above 873 K by J(H2) = (7 +/- 2) mol.m(-2).s(-1) exp[(-30.3 +/-2.5) kJ.mol(-1)/(RT)].