A pump arrangement includes an axial-flow machine and a drive to convey fluid mounted in a housing. The axial-flow machine is formed by at least one first rotor having permanent magnets, a shaft connected to the first rotor and a stator arrangement with stator teeth distributed concentrically around the shaft axis circumferentially and axially separated from the first rotor by an air gap. The stator teeth have axially-opposite end portions and a tooth core therebetween wound with at least one coil winding. The second end portion, turned away from the first rotor, of each stator tooth forms a tooth root joined to a back plate. The first rotor is an eccentric disk and on the side away from the stator arrangement has an eccentric cam, radially spaced from the shaft axis, and rotatably and torque-transmittingly connected to the drive. An axial-flow machine and a compressor includes the pump arrangement.