Multiphase machines have been attracting more and more attentions in high-reliability-required applications due to their inherent fault-tolerant capability. Postfault control strategies with-standing open-circuit faults (OCFs) for several multiphase machine types, like five-phase, symmetrical six-phase (S6) and asymmetrical six-phase (A6) machines, have been widely investigated in recent literatures. However, fault-tolerant control for symmetrical dual three-phase (D3) machines have rarely been studied so far. To fill the gap, this paper addresses key issues in postfault decoupling modeling and field orient control (FOC) for the dual three-phase surface-mounted permanent magnet synchronous machine (SPMSM) with isolated neutrals under single-phase OCF. To do so, a postfault decoupling model with reduced-order transformation is established for D3 machines. Postfault current references are reconfigured with two main-stream criteria: minimum-loss (ML) and maximum-torque (MT). Furthermore, third harmonic flux linkage/back-EMF are taken into account in modeling and control, since it causes third harmonic currents and hence torque ripples under single-phase OCF. Proportional-resonant controllers are employed to decrease the third harmonic currents and torque pulsations. The validity of the postfault control strategies is proved by experiments.