A device for the free-form bending of longitudinal profiles, in particular pipes, in which an axial sleeve is arranged downstream of a feed unit in its direction of feed. Arranged downstream of the axial sleeve in the direction of feed, is a bending sleeve. The feed unit and the axial sleeve in each case have a drive pointing in the direction of feed, wherein the axial sleeve can be adjusted independently of the feed unit. The feed unit and the axial sleeve further have rotary drives for the simultaneous rotation in the same direction of the longitudinal profile held and guided by them. The bending sleeve can only be adjusted in a translatory manner by means of a drive in an axis running transverse to the axis of the longitudinal profile and the feed device. In addition to this, it can be pivoted by means of a drive about an axis lying transverse to the axis of the longitudinal profile and the feed device. The bending sleeve is additionally mounted so as to freely rotate in sympathy with the guide sleeve or is braked in relation to it.