An adapter sleeve has an external layer for supporting a printing cylinder carrying data and/or images to be printed. The adapter sleeve has an internal layer defining a bore enabling the sleeve to be mounted onto a rotary mandrel of a printing machine. Each opposite extreme end of the adapter sleeve includes a rigid, load-bearing, radial spacer member disposed between the layers to provide rigidity and indeformability during the use of the sleeve with time. The inner surface of each of the extreme end radial spacer members is defined by rigid and non-deformable material of very low coefficients of dynamic and static friction.