Multiphase flux-switching permanent-magnet (FSPM) machines inherit the merits of conventional FSPM machines and the common advantages of multiphase machines, e.g., low torque pulsations, a high torque density, and a high fault-tolerant capability. When a hybrid excitation is applied, postfault armature currents can be reduced by applying a positive field current (PFC). Hence, in this paper, based on both 2-D and 3-D finite-element analyses (FEAs), two six-phase hybrid-excited flux-switching (HEFS) machines with E-core and C-core stator laminations are designed, respectively. Iron bridges are adopted in each machine, and the influences on the performance are investigated. In addition, alternative-tooth-wound armature windings are employed in the C-core machine to obtain physical and magnetic isolations between armature phases. A comprehensive comparison of the two designs is carried out. Then, more attention is paid to fault-tolerant operating capabilities when an open-circuit fault occurs to only one phase and two phases of armature windings, respectively. The PFC can be applied in the C-core machine under fault-tolerant operating conditions; thus, the postfault armature current can be reduced while maintaining the torque output. Overall, the torque output can be effectively maintained in each HEFS machine during postfault operations. Finally, the FEA-based studies are validated by experimental measurements on two HEFS machine prototypes.