Abstract: The apparatus comprises: a running conveyor (1) with hooks (2) for suspending a set (5) of organs by the diaphragm (6) and conveying it in a conveying direction of the conveyor (1); a slit device (10; 11) arranged below the conveyor (1) with a slit (13; 44) for guiding horizontally in the slit a connective tissue part (9; 6) of the set (5) of organs during the conveyance of the set of organs on the conveyor with an organ (8; 7) located below the slit (13; 44), a retaining device (14-16; 40) arranged in a conveying path which the organ (8; 7) follows with the connective tissue part (9; 6) guided by the slit (13; 44), the retaining device (14-16; 40) being adapted to retain the organ (8; 7) on the retaining device by the conveyor's (1) pull in the set (5) of organs; and (22, 23; 49-51, 54) for causing separation between the organ (8; 7) and the connective tissue part (9; 6) when such retention has been provided.