Electric machines play an important role in modern energy conversion systems. This paper presents a novel brushless fault-tolerant flux-modulated memory (FTFM) machine, which incorporates the merits of a flux-modulated permanent magnet machine and multi-phase memory machine and is very suitable for applications that require wide speed ranges of constant-power operation. Due to the magnetic modulation effect, the FTFM machine can produce a large torque at relatively low speeds. Due to the usage of aluminum-nickel-cobalt (AlNiCo) magnets, this machine can readily achieve a flexible air-gap flux controllability with temporary DC current pulses. Consequently, the constant-power region is effectively expanded, and the machine\'s efficiency during constant-power operation is increased. Due to the multi-phase armature winding design, the FTFM machine enables lower torque ripple, increased fault tolerance ability and a higher possibility of splitting the machine power through a higher number of phases, thus the per-phase converter rating can be reduced. The design methodology and working principle of this kind of machine are discussed. The electromagnetic performances of the proposed machine are analyzed using the time-stepping finite element method (TS-FEM).