We report an experimental attempt to measure resistively the predicted periodic reentrant behavior of small superconducting loops in external magnetic fields. The superconductivity in the contact probes was deliberately weakened in order to minimize their influence on the loops. As expected, the loops exhibit Little-Parks oscillations near the top of the resistive transition. At lower temperatures, instead of the reentrant behavior, the samples show an unexpected negative magnetoresistance. We interpret this result as being due to a nonequilibrium situation existing between normal and superconducting regions in the sample. © 1989 The American Physical Society.