A variator (10) has two races (12, 12) mounted for rotation about a common axis. Opposed, shaped faces (14, 18) of the races define an annular space containing at least one roller (38, 40) which runs upon the races to transfer drive between them. The roller is mounted on a carrier (42, 44) in such a way that its inclination to the common axis is able to change, to enable changes in variator ratio. The rollers and their carriers are controlled through a mechanism comprising a sun (46, 48) and a ring (50, 52) with which the carrier engages. Relative rotation of the sun and ring causes a tipping motion of the carrier (42, 44), so that the rollers steer themselves to a new inclination. To control the sun and ring, there is provided a planet (100) which engages them both. The rotational position of the carrier is controlled independently of its engagement with the sun and the ring.