Universal conductance fluctuations in wires and Aharonov-Bohm oscillations in loops are not symmetric about H=0. The observation of asymmetry in the periodic oscillations is possible when the phase-coherence length of the wave function is comparable to the separation of the voltage probes. In both cases, four-probe measurements yield resistances which depend on lead configuration. The asymmetries appear like Hall voltages, and are consistent with Onsager's relations. © 1986 The American Physical Society.