An apparatus for controlled motion of one or more printing units designed for printing images on one or more faces of a sheet material, such as paper or cardboard, that is designed to move in a feeding direction defining a longitudinal axis, which apparatus is adapted to be associated with a machine for cutting and creasing customized packages, and comprises: - a stationary frame defining an elongate transverse axis, and having transversely spaced end areas (32, 33), said frame having a top surface, defining a slide plane (π) for the sheet material which is substantially coplanar with the feeding plane of the machine; - at least one box-like support for a corresponding printing unit, which is slidably mounted on transverse guide means integral with said frame, said support is accommodated in a transverse seat formed in the frame and having the transverse guide means mounted therein; - drive means for controlled motion of said at least one box-like support along said transverse guide means, said drive means comprising a belt section and at least one powered roller associated with said support; - a belt comprising at least one flexible stationary section having a predetermined length, end portions stably secured to said end areas (32, 33) of said frame, and a corresponding intermediate portion which is partially wound on said powered roller for the rotation of the latter to promote the movement of said support relative to said belt section; characterized in that said belt is open with free ends (28, 29) stably fixed to corresponding end areas (32, 33) of the frame, said belt section having an outer surface and two or more substantially straight portions (55, 56, 57) parallel to the ground and designed to close the top of the seat of the frame in which the support is slidingly mounted so that said outer surface is substantially coplanar with said slide plane (π) to prevent the sheet material from encountering gaps or voids in its feed direction and from sticking at the seat. - a stationary frame defining an elongate transverse axis, and having transversely spaced end areas (32, 33), said frame having a top surface, defining a slide plane (π) for the sheet material which is substantially coplanar with the feeding plane of the machine; - at least one box-like support for a corresponding printing unit, which is slidably mounted on transverse guide means integral with said frame, said support is accommodated in a transverse seat formed in the frame and having the transverse guide means mounted therein; - drive means for controlled motion of said at least one box-like support along said transverse guide means, said drive means comprising a belt section and at least one powered roller associated with said support; - a belt comprising at least one flexible stationary section having a predetermined length, end portions stably secured to said end areas (32, 33) of said frame, and a corresponding intermediate portion which is partially wound on said powered roller for the rotation of the latter to promote the movement of said support relative to said belt section; characterized in that said belt is open with free ends (28, 29) stably fixed to corresponding end areas (32, 33) of the frame, said belt section having an outer surface and two or more substantially straight portions (55, 56, 57) parallel to the ground and designed to close the top of the seat of the frame in which the support is slidingly mounted so that said outer surface is substantially coplanar with said slide plane (π) to prevent the sheet material from encountering gaps or voids in its feed direction and from sticking at the seat.