A coaxial pump or turbine module includes an integral, modular motor or generator comprising a magnet structure containing radial or axial permanent magnets and/or induction coils detachably fixed to a rotor, and a stator housing detachably fixed to the module housing. Working fluid is directed axially through a flow path symmetrically distributed within an annulus formed between the module housing and the stator housing. The stator housing can be cooled by the working fluid, or by a cooling fluid flowing between passages of the flow path. The flow path can extend over substantially a full length and rear surface of the stator housing. A plurality of the modules can be combined into a multi-stage apparatus, with rotor speeds independently controlled by corresponding variable frequency drives. Embodiments include guide vanes and/or diffusers. The rotor can be fixed to a rotating shaft, or rotate about a fixed shaft.