The razor has a forward roller (10) which is parallel to a rear roller (20) and a third roller (4) at the side. The roller at the side is driven by friction contact with the forward roller which then transmits rotation to the rear roller so that it rotates in the same direction as the forward roller when the razor is pulled over the skin. Removable blades (61,62) are mounted within a blade housing (60) and are parallel to the forward and rear rollers. The floor (63) of the blade housing is made from a flexible plastic and has two hooks (64,67) which engage with projections (51,52) on the shaft to lock the blade housing in position.