The letterpress printing machine comprises an impression cylinder (8), at least one inking device (11, 12, 13) with an inking train comprising inking rollers (25, 26, 28) and at least one letterpress forme cylinder (14, 15, 16) inked by said at least one inking device (11, 12, 13). Said at least one letterpress forme cylinder (14, 15, 16) is driven by first drive means (30), whereas said at least one inking device (11, 12, 13) is driven by second drive means (31, 32, 33), said second drive means (31, 32, 33) being mechanically independent from said first drive means (30). A control unit is coupled to the second drive means (31, 32, 33) to adjust a circumferential speed of the inking rollers (25, 26, 28) with respect to a circumferential speed of the letterpress forme cylinder (14, 15, 16) so as to adjust deposition of ink by the inking device (11, 12, 13) on the letterpress forme cylinder (14, 15, 16). At least one of letterpress forme (14, 15, 16) cylinder is preferably a numbering cylinder for numbering printed sheets or webs.