In a high-gradient magnetic separator for the selective separation of magnetic particles from a suspension which is conducted through a matrix of plate-like separation structures of a magnetic material which are disposed in a magnetic field and through which the suspension is conducted, alternate plates of the separation structures are movable relative to the other plates which are stationary and are all mounted on a carrier by which they can be moved relative to the stationary plates at least during cleaning of the plates for the removal of magnetic particles collected on the plates.