An apparatus for applying a cosmetic, such as mascara to eyelashes, includes a handle, a stem, and an applicator head coupled to the stem and supported for movement relative to the handle in a direction substantially parallel to the stem axis. An actuator moves the applicator head in an axial motion comprising a forward stroke and a reverse stroke. Additionally or alternatively, the actuator may move the applicator head in a composite motion including an axial component substantially parallel to the stem axis and having a forward stroke and a reverse stroke, and a rotational oscillating component. The actuator may be a motor having a rotating motor shaft, and the applicator may further include a transmission coupling disposed between the motor shaft and the applicator head for automatically converting rotation of the motor shaft in one direction into axially reciprocating movement of the applicator head.