In this paper, the propagation of a second-order cylindrical vector beam in gradient-index and microstructured fibers is numerically simulated using the RSoft Fullwave software. The second-order vector beams are shown to be vector modes of these fibers. In the calculated fundamental modes, regions are found in which there is an energy flow directed oppositely to the beam propagation direction (regions of a reverse energy flow). The absolute value of the longitudinal component of the reverse energy flow is found to be much lower than that of the forward flow.