Abstract: Described is a process and apparatus for printing on metal hollow bodies therearound, in particular a can body, by means of thermal transfer printing, wherein color particles disposed on an auxiliary carrier are introduced under the application of heat and pressure by diffusion for example into a dyestuff-affinitive layer on the can body. The process and apparatus are such that the can body is briefly heated with the auxiliary carrier applied thereto and the transfer process which is iniated in that way is then brought to a conclusion at a preferably falling temperature. That provides visually sharp images on the can body, by suppression of the lateral migration of the dyestuff molecules during the transfer operation, to provide a satisfactory closed printing effect at the overlap region of the auxiliary carrier.