An apparatus (AS) measures positions of marks (202) on a lithographic substrate (W). A measurement optical system comprises illumination subsystem (504) for illuminating the mark with a spot of radiation (206) and as detecting subsystem (580) for detecting radiation diffracted by the mark. The substrate and measurement optical system move relative to one another at a first velocity (vW) so as to scan the mark while synchronously moving the spot of radiation relative to the reference frame (RF) of the measurement optical system at a second velocity (vSPOT). The spot scans the mark at a third velocity (vEFF) which is lower than the first velocity to allow more time for accurate position measurements to be acquired. In one embodiment, an objective lens (524) remains fixed in relation to the reference frame while a moving optical element (562) imparts the movement of the radiation spot relative to the reference frame.