Two-dimensional organic τ-type conductors show metallic temperature dependence of resistivity down to T min =30–50 K, below which a resistivity upturn is observed. A large negative magnetoresistance appears below T min suddenly in temperature. Below about 4 K, magnetoresistance in any direction is extremely hysteretic in field-, temperature- or field-angle-sweep, and ρ ⊥( H//plane) shows switching between two- and four-fold depending on magnetic and thermal history, indicating magnetic domain generation. Static susceptibility shows slight ferromagnetic component. NMR is in favor of anti-ferromagnetism below about 15 K. These two results imply that the system is a weak ferromagnetic one. Preliminary optical reflectance and specific heat studies implied metallic state at low temperature, but no clear-cut proof has been shown whether or not the ground state is metallic. This report presents giant Shubnikov de Haas (SdH) oscillation in both τ-(EDO- S, S-DMEDT-TTF) 2(AuBr 2) 1+ y , and τ-(P- S, S-DMEDT-TTF) 2(AuBr 2) 1+ y , ( y∼0.75), which is a clear evidence for the metallic ground state. However, the observed Fermi surfaces (FS) are 0.65 and 6.1% of the first Brillouin zone for τ-(EDO- S, S-DMEDT-TTF) 2(AuBr 2) 1+ y , and 2.3 and 6.9% for τ-(P- S, S-DMEDT-TTF) 2(AuBr 2) 1+ y , ( y∼0.75), which suggest extremely small FS pockets, and were not expected by the previous band calculation. Further, it is surprising that the Dingle temperature was around 1 K, indicating unexpectedly clean, while residual resistivity ratio is about 1. We note that the fundamental oscillation of 0.65% is already n=2 state, which is already next to the Landau quantum limit.