The invention relates to devices in a printing couple (04) of a printing machine, at least comprising at least one roll (12; 12.1; 12.2; 12.3), which is mounted axially movably on both sides in side frames (30), of an inking system (08) or damping system (09) of the printing couple (04), to which roll a temperature control agent can be fed on an end face via an interface (24) for controlling the temperature of the roll, wherein at least one transversing drive (22) for generating an axial transversing stroke of the roll (12; 12.1; 12.2; 12.3) and at least one drive means (18) for generating a rotatory movement of the roll (12; 12.1; 12.2; 12.3) are provided. The rotatory drive means (18) and the transversing drive (22) engage with same end face of the roll (12; 12.1; 12.2; 12.3) opposite of the interface (24). Between the roll (12; 12.1; 12.2; 12.3) and the rotatory drive means (18), a coupling (27) comprising two rotors (41, 42) that can be moved axially relative to each other are provided, for compensating for the transversing stroke caused by the transversing drive (22). A first of the rotors (41, 42) is mounted rotatably in or on the side frame (30), however mounted in a stationary manner with respect to an axial direction and is mechanically coupled to the drive means (18) for the rotatory drive thereof. The second of the rotors (41, 42) is connected to a journal (28) of the roll (12; 12.1; 12.2; 12.3) in a non-rotational, tension-resistant and compression-resistant manner.