A process carried out by an ink-jet printing apparatus (1) comprises the steps of placing articles (3a) to be printed on a support (12) of an apparatus (1) further provided with a carriage (6) carrying at least one main print head (8) and at least one auxiliary head (11), and moving the support (12) and the carriage (6) relative to each other in at least one first ink-laying direction (X). The process is put into practice by carrying out the following steps in succession: laying the ink emitted from the auxiliary print head (11) to carry out printing of the articles (3a, 3b) with a background layer, drying the ink just laid by the auxiliary head (11) through a first drying device (14) disposed alongside the main head (8) and laying the ink emitted from the main head (8) to carry out decorations on the background layer.