This paper deals with the control of two five-phase permanent magnet synchronous motors (PMSMs), which are connected in series and operating at different speeds and torques. The topology under study is intended for use in an electrical naval propulsion system. The backstepping control strategy, which uses the Lyapunov stability concept, is employed to control the speed of the two machines considering the series connection of the PMSM stator windings. A comparative study, with respect to classical Vector Control (VC) using PI regulators, is provided to demonstrate the robustness of the proposed control strategies in both healthy and faulty conditions. Typically, dual PMSMs in series cannot operate in the degraded mode in the event of faults. This study optimizes their operation by adapting to such modes, including faults caused by symmetrical parameter changes or by an asymmetrical High Resistance Connection (HRC) in the stator windings, thereby ensuring continuity of service. The HRC is investigated and verified in one stator phase, in two adjacent stator phases and in two non-adjacent stator phases, as well as in a symmetrical HRC fault across all phases. Matlab-based simulation results validate the control design to achieve the desired performance and prove the effectiveness and the asymptotic stability of backstepping control for two series-connected 5-Փ PMSMs, thereby providing redundancy for the naval electric propulsion system.