This paper presents two novel designs of magnetic flux-modulated mnemonic (MFMM) machines which incorporate magnetic gearing effect and flux-mnemonic concept together. Both of these two machines can perform large torque production at low-speed because of the magnetic gearing effect, and can readily achieve flexible fluxcontrollability by temporarily applying current pulses to magnetise/demagnetise aluminium-nickel-cobalt magnets so as to expand the constant-power region operation effectively. One machine has permanent magnets (PMs) on its rotor and outer stator which is referred as the dual-layer PM MFMM (DPM-MFMM) machine; bi-directional field modulating effect is artfully incorporated in this machine to guarantee effective coupling between the magnetic fields excited by the armature windings and those excited by the two sets of PMs. The second machine employs all the PMs on the outer stator and the rotor is only made up of ferromagnetic segments. In other words, it is a single-layer PM-MFMM (SPM-MFMM) machine, and the rotor carries the flux modulating poles. The configurations and working principles of both machines are discussed. The electromagnetic performances are comprehensively studied and quantitatively compared using finite element method (FEM).