Abstract: A rotary steering apparatus for a drill string in which a bending section induces a bend in a portion of the bottom hole assembly of the drill string by using the rotation of the drive shaft that drives the drill bit during normal drilling, while operating at a reduced or zero drilling mud flow rate, to drive a reduction gear that rotates a nut or cam so as to place a tension tube into tension. The tension tube abuts a flexible housing and places the flexible housing in compression. The flexible housing has a local weakening formed in it that causes it to preferentially bend in a predetermined direction. Compression in the flexible housing causes the housing to bend, which bends a portion of the bottom hole assembly so as to alter the direction of drilling. Rotation of the drive shaft at reduced or zero mud flow rate also causes the drive shaft to drive rotation of a second reduction gear the output of which rotates the bent portion of the bottom hole assembly thereby altering its tool face angle.