Apparatus for grouping a number of units, such as packaging units, when palleting the units, comprising a feed belt for conveying the units (10) and a grouping belt, which defines a grouping plane, said feed and grouping belts being driven for movement parallel to one another, and a robot, which is designed to group the units by positioning and orienting the units on the grouping plane. At least one part of the feed belt (1) runs beside and adjacent to the grouping belt (2). The robot (3) is a multi-axial industrial robot having a robotic arm on which a pusher element (5) is arranged, rotatable about an axis (6) perpendicular to the grouping plane, in order to allow the transfer of at least one unit from the feed belt to the grouping belt under a pushing action supplied by the pushing element, together with orientation and positioning of the unit on the grouping belt.