There is described a printing press (1; 1*; 1**) comprising an ink-receiving cylinder (9; 8) receiving ink from an inking system (90-93, 90*, 93*; 95-99, 95*, 99*; 100-104, 100*, 104*) having a plurality of ink-applying cylinders or rollers (93, 93*; 99, 99*; 104, 104*) arranged one above the other around part of a circumference of the ink-receiving cylinder (9; 8), the ink-applying cylinders or rollers (93, 93*; 99, 99*; 104, 104*) being inked by a corresponding plurality of inking devices (90, 90*; 95, 95*; 100, 100*), the printing press (1; 1*; 1**) further comprising an inking carriage (52; 55; 57) supporting the plurality of inking devices (90, 90*; 95, 95*; 100, 100*), which inking carriage (52; 55; 57) can be moved with respect to the ink-receiving cylinder (9; 8) between a working position and a retracted position. The at least one selected inking device (90*; 95*; 100*) amongst the plurality of inking devices (90, 90*; 95, 95*; 100, 100*) of the inking system (90-93, 90*, 93*; 95-99, 95*, 99*; 100-104, 100*, 104*) is supported onto the inking carriage (52; 55; 57) via a movable frame (60; 65; 70), which movable frame (60; 65; 70) is supported by the inking carriage (52; 55; 57) to allow movement of the selected inking device (90*; 95*; 100*) with respect to the inking carriage (52; 55; 57) and with respect to a remaining part (90; 95; 100) of the plurality of inking devices (90, 90*; 95, 95*; 100, 100*).