A handpiece of an electric toothbrush having a housing in which a drive unit is received. The housing has a forward or rearward housing opening adapted to be closed by a cover in a preferably moisture- and liquid-proof manner, with snap-action detent elements provided on the housing and/or the cover for locking the cover on the housing with a snap action. A combination of snap-fitting and threaded engagement releases the snap-fitting engagement between the cover and the housing.