A dental handpiece in which supply lines run axially inside a longitudinal sleeve. This sleeve and the supply lines are divided transversely to form several handpiece sections. Each one of two facing ends of two adjacent handpiece sections have an axially projecting sleeve into which the end of the other handpiece section can be inserted. Two ends of the adjacent handpiece sections have a screw thread each. The thread may be an inside thread of the projecting sleeve forming a pipe-stub or nipple like threaded portion of the end inserted in the sleeve of the other handpiece section. One of the two pipe-stub like threaded portions has at least one cutout extending axially from its free end and is radially spring-like pretensioned in the unthreaded state of the two adjacent handpiece sections away from the other threaded portion with threads not engaged. This one of two pipe-stub like threaded portions, furthermore is rotatable relative to one engaging portion of the handpiece section which has a threaded portion with at least one cutout about an axis of the latter.