  We show in the case of a superconducting Nb ladder that a mesoscopic
superconductor typically exhibits magnetoresistance oscillations whose
amplitude and temperature dependence are different from those stemming from the
Little-Parks effect. We demonstrate that these large resistance oscillations
(as well as the monotonic background on which they are superimposed) are due to
{\it current-excited moving vortices}, where the applied current in competition
with the oscillating Meissner currents imposes/removes the barriers for vortex
motion in increasing magnetic field. Due to the ever present current in
transport measurements, this effect should be considered in parallel with the
Little-Parks effect in low-$T_c$ samples, as well as with recently proposed
thermal activation of dissipative vortex-antivortex pairs in high-$T_c$
samples.
