A positioning device comprising a first part (1) which is movable relatively to a second part (2) in an X-direction and a Y-direction, said first part (1) comprising a carrier (5) on which a system of magnets (3) is arranged according to a pattern of rows (7) and columns (8) extending parallel to the X-direction and the Y-direction, respectively. The magnets in each row and column are arranged according to a Halbach array, i.e. the magnetic orientation of successive magnets in each row (7) and each column (8) rotates 90° counter-clockwise. The second part (2) comprises an electric coil system (4) with two types of electric coils (C1, C2), one type having an angular offset of +45°, and the other type having an offset of −45° with respect to the X-direction. The magnet configuration causes a very strong magnetic field.