A magnet pump for an auxiliary unit of a vehicle includes an inlet, an outlet, an electromagnet comprising an armature, a core, a coil and a yoke, a cylinder comprising an outlet opening, and an axial piston which moves in the cylinder. The axial piston includes first and second axial piston parts, a gap arranged between the first and second axial piston parts, and an axial through bore. A first non-return valve is biased between the first and second axial piston parts and against the axial piston. A second non-return valve is biased against the outlet opening of the cylinder. The first axial piston part is connected with/is integrally formed with the armature and is lifted off the second axial piston part. A fluidic connection exists between the inlet and the outlet via the gap when the first axial piston part is lifted off the second axial piston part.