Two novel phenomena were observed in steady and transient shear measurements which were made in a Couette device of a R-17 Weissenberg Rheogoniometer with suspensions of polystyrene spheres, 40-50 mu m in diameter, suspended in a mixture of silicone oils at volume fractions 0 less than equivalent to phi 0. 55. When phi greater than equivalent to 0. 3, the steady-shear viscosity at a given shear rate was found to drift for many hours to an asymptotic value which, in contrast to the scatter of the initial measurements, was very reproducible. Again, when phi greater than equivalent to 0. 3, the shear stress showed a memory for the direction of previous shearing when the shear was stopped for a while and then restarted with either the same or the opposite sign. Moreover, during oscillatory shear experiments, these suspensions exhibited a nonlinear response which in fact could be predicted from their response to a sudden reversal of the direction of steady shear.