We have directly observed current-dependent, nonlinear contributions to the conductance fluctuations of phase-coherent metallic wires and loops. The fluctuations in the current-voltage curves are reproducible, asymmetric about I=0, and in qualitative agreement with theoretical predictions. In ac measurements, the nonlinear terms also generate large harmonic signals of the conductance fluctuations whose dependence on the drive current can be understood qualitatively. The spectra of harmonics from loops and wires have different dependences on the voltage across the sample. © 1988 The American Physical Society.