Low-strength clay minerals are a common constituent of fault gouges, and are often cited as a possible explanation for the low ambient shear stresses along the San Andreas fault inferred from heat flow constraints and in situ stress measurements. Montmorillonite, the weakest of the clay minerals, undergoes a gradual phase transition to illite with depth. In order to compare the shear stresses supported by these two minerals with those thought to exist along the San Andreas, we have measured the frictional sliding behavior of pure montmorillonite, mixed montmorillonite/illite and pure illite as a function of effective pressure, simulating burial to seismogenic depths. Strength measurements verify that the effective pressure law for friction holds for these minerals under all conditions. That is, the measured stresses were a function of the effective pressure, P_c - P_p, independent of the choice of confining and pore pressure. This relation, common for many other rock types, was previously untested for these clays under most conditions. Results show that dry samples were consistently stronger than saturated samples, and that strength increased with increasing illite content. In addition, the coefficient of friction increased as a function of pressure for the montmorillonite gouge, but was independent of pressure for the illite gouge. This behavior may be explained by the presence of loosely bonded interlayer water in the montmorillonite, which is squeezed out at higher pressures, changing the frictional characteristics of the clay. The nonexpanding illite was not affected in this way. For the montmorillonite-to-illite compositional profile, an average shear stress of 60 MPa was determined for crustal conditions to 15 km, assuming a normal hydrostatic gradient. If montmorillonite remains stable at depth, the resulting average shear stress is reduced to 30 MPa. In either case, these values are above the 10-20 MPa shear stress limit along the San Andreas inferred from heat flow constraints. Strength may be reduced to in-situ levels if fluid pressures become greater than hydrostatic within the gouge zone.