An apparatus comprises transferring means (9) for transferring objects (8) obtained by compression-moulding doses of plastics (D) from forming means (7) of a forming unit (5) and supporting means (2) for rotatably supporting said transferring means (9). In order to avoid blows and/or damage between said transferring means (9) and said forming means (7), the apparatus comprises moving means (3) connected to said supporting means (2) and configured for moving said transferring means (9) at least between a first operating position (A) nearer said forming unit (5), in which said transferring means (9) interacts with said forming means (7) to transfer said objects (8), and a second operating position (B), in which said transferring means (9) is spaced away from said forming unit (5) so as not to interact with said forming means (7). The movement of said transferring means (9) from said first operating position (A) to said second operating position (B) has at least a component in the same direction as a tangential component of the rotational motion of said forming unit (5) in said first operating position (A).