A device for shaving hair, comprising a base portion having a grip, at least one cutting member having a cutting edge and a cutting direction, and an actuator for effecting a periodical motion of the cutting member relative to the base portion, characterized in that the periodical motion is affected substantially in an imaginary plane extending transversely to the cutting edge and has a first motion portion and a second motion portion following the first motion portion, the first motion portion being mainly directed in the cutting direction, and the second motion portion being mainly directed opposite to the cutting direction and being closer to the skin, during operation, than the first motion portion, the periodical motion is a substantially elliptical motion having a major axis and a minor axis, the major axis being mainly directed parallel to the cutting direction, and that the cutting member is mounted to a carrier which is driven by the actuator via a transmission comprising a first and a second eccentric member which are driven by the actuator at equal rotational speeds about separate axes of rotation extending parallel to the cutting edge, said first eccentric member having a fixed position relative to the carrier in a direction parallel to the major axis and a free position relative to the carrier in a direction parallel to the minor axis, and said second eccentric member having a free position relative to the carrier in a direction parallel to the major axis and a fixed position relative to the carrier in a direction parallel to the minor axis.