An apparatus (1) for controlled motion of one or more printing units (2) designed for printing images (I) on one or more faces (F) of a sheet material (M) that is designed to move in a feeding direction defining a longitudinal axis (L). The apparatus (1) is adapted to be associated with a machine (3) for cutting and creasing customized packages and comprises a stationary frame (10) defining an elongate transverse axis (T), at least one box-like support (12) for a corresponding printing unit (2), which is slidably mounted on transverse guide means (13) integral with the frame (10), drive means (26) for driving the box-like support (12) along transverse guide means (13), the drive means (26) comprise at least one section of a stationary and flexible belt (27) having a predetermined length (I) and end portions (28, 29) stably secured to the frame (10), as well as at least one powered roller (31) associated with the support (12), and having an intermediate portion (30) of the belt section (27) at least partially wound thereon for its rotation to promote the movement of the support (12) relative to the belt section (27). A machine (3) for cutting and creasing customized packages, comprising the apparatus for driving the printing units (2).