A rotary hair-cutting unit including an internal cutting member having cutting elements with cutting edges, and an external cutting member having hair-guiding elements with counter-cutting edges). The co-operating edges define a shearing angle, such that during rotation a cutting edge first meets a counter-cutting edge at a radial initial-passing position. In a cross-section at said radial initial-passing position one of the internal cutting member and the external cutting member is provided with a particular abutment geometry. The inclusion of an abutment geometry will be effective to push the depressed hair-guiding element and the rotating cutting element axially away from one another, such that the cutting element will pass the hair-guiding element without being blocked and without causing substantial collision damage.