A process and also to a system for cleaning and maintaining a medical hand-held instrument, in particular a dental hand-held instrument, with an elongate grip sleeve in which elements are arranged which pertain to a drive arrangement and which are, in particular, rotatably supported, for example a shaft. For the purpose of cleaning and maintaining the hand-held instrument different media are conducted through it. In this connection a first medium, for example oil, is conducted merely through a power-transmission region surrounding the elements of the drive arrangement, whereas, on the other hand, a second medium, for example a cleaning agent, is conducted additionally also through at least one further cavity within the hand-held instrument.