We have observed resistive branches in the I-V characteristics of long Josephson junctions which can be simply understood in terms of the motion of individual Josephson fluxoids with reflection as antifluxoids at the junction edges. The characteristics of these resistive branches differ qualitatively from those of the current singularities previously reported by Chen et al. and by Fulton and Dynes. Our results indicate that the current singularities are not simply related to the motion of individual fluxoids. © 1980 The American Physical Society.