Abstract: There is provided an apparatus for determining the position of objects (2) advancing in line on a supporting plane belonging to a transport line (1). The apparatus includes, for determining the position of an object (2) on the supporting plane, sources (22A, 23A) of a first and a second light beam (220, 230) generating collimated beams (220, 230) with substantial point-like cross-sectional size, which propagate along paths defining a plane parallel to the supporting plane and forming acute angles with the advance direction (F), and detectors (22B, 23B) for the separate detection of the first and the second beam (220, 230). A processing unit (12) includes means for comparing the instants at which an object passes through each beam (220, 230) and for detecting, based on the comparison result, a possible offset of the position of the object (2) from a reference position.