Sequences of spatially interchanging 0- and π-shifted Josephson junctions are encountered in superconductor-ferromagnet-superconductor heterostructures, asymmetric grain boundaries in thin films of YBCO, and YBCO/Nb zigzag junctions. In this paper we demonstrate existence of Josephson vortices in applied fields much higher than the Josephson penetration field. The high-field vortices exist in narrow field intervals near equidistant fields H_n. When the applied field is in any of these intervals, the flux per junction is nø ₀, where n in an integer. We show that high-field vortices are much longer than the vortices carrying flux in each of the 0- or π-shifted junctions. As a result the field within the vortices is much lower than the background field. High-field vortices carry one flux quanta or half-flux quanta and are free to move, unlike the semi-fluxons in low fields that are pinned by the contacts between 0- and π-junctions. In the presence of a transport current the high-field vortices are subjected to the Lorentz force and move to one side of the chain, reflect, move to the other side, etc. This periodic motion generates constant voltage across the chain with resonances similar to the zero-field-steps. If the vortices carry half-flux quanta, the resonances will appear at half the voltage one would expect for zero-field-steps.